My advice would be to go to as many stores as you can. Don't buy anything right away. Play as many guitars and amps as you can. Eventually you will find one that you know was built for you; kind of like looking for a new puppy - when you find the right one you know it, it is evident, there is no question in your mind. But you have to look around and play a lot of different guitars. You might want to buy more than one but if you want to start with one don't be afraid to spend some money for a good one. Obviously you have been playing acoustic for a while.
The amp is just as important for the sound as the guitar or more important. A great amp will make even a junk guitar sound great; a great guitar will sound like junk thru a junk amp. You sort of have to find a financial balance where you get a good guitar and a good amp, because you need both in order to get a good sound.
Fender makes an all purpose type little tube amp called a Super Champ XD that costs 299 US new from the big internet places.
A suggestion for a great guitar is the Les Paul copies made by Agile and sold thru http://www.rondomusic.com , no affln. The Agile Les Paul copy type guitars are very good guitars and definitely excellent beginner electric guitars and some even come with Bigsby's on them. Check out their web site. Many say that the Agile AL-3000 and above models are way better than the cheaper AL 2000's and 2500's, but I think the cheaper versions are great guitars. I have an AL 3100 cherry sunburst flammed maple double bound body one that sounds great stock, no need to upgrade anything.
Speaking of tremolos on guitars, Fender makes a great simple spring counterbalanced tremolo that has been a landmark of electric guitar history and still exists today in its refined but essentially the same form. Many players like Fender Stratocasters for their variety of sounds and the trem. You can get them with quiet noiseless pickups, because, unlike humbucker equipped guitars like a lot of the Les Paul types, a lot of typicallly available stratocasters have "single coil" pickups that have a distinct sound but produce some background noise when not strumming the strings, called sixty cycle hum in the US and some other electrical frequency in other parts of the world, but noticeable as a hum thru the amp that gets louder the louder you turn up your amp. This hum can be undesirable to some players and they often prefer to get "humbucking" guitars equipped with humbucker pickups - these are very quiet and stronger pickups that send a stronger signal to the amp, sounding louder and more full at the same amp volume, often, and are noiseless. The Agile Les Paul types are humbucking guitars in general, although they have single coil versions for those that prefer the single coil sound and are not unimpressed with the accompanying hum.
The hollow body and semi-hollow body electrics have a different sound from the solid body electrics. Solid body electrics are more removed from the acoustic guitar in sound and playability, and are a more modern evolution of the electric guitar, although the modern day hollow and semi-hollow body guitars have evolved quite a bit since they first carried electric pickups.
I would say the bottom line is to "get what YOU want". You are paying for it. You are the customer. Avoid pressure from other people and salesmen. Play a bunch of them, sleep on it before you make a decision. Think it thru and try to pick out the one that you really bond with, regardless of color and style. Sometimes the best guitars "pick you out" rather than you picking them out. Don't be surprised if you wind up getting something you didn't have the faintest idea you might like. The same goes with the amps. Listen to them closely and don't be afraid to turn them up - you are the customer. Pay attention to the "feel" of the guitar in your hands and how the chords fall into place - there is a lot of difference in how the guitars feel, especially the necks and fretboards. The Agile Les Paul types feel good to most people that talk about them on the forums. If you buy one of these, at a great price and a very excellent value, you will not get a chance to try one out anywhere most likely, but the company has a very reasonable return policy so you can try a different style one and so on. Although this is time consuming sending guitars back and forth, the same could be true for a guitar that you bought locally and had to return for repairs. Lots of times these have to be sent out for repair and you wouldn't be any farther ahead doing this than getting an Agile. Most Agile guitars, however, are received by their owners in perfect condition and the quality control is claimed to be superior to many of the big name similar guitars costing a few hundred dollars more, or more. I have no affln. with Agile or it's distributor. I am just mentioning them because you may not know about them and you asked for suggestions.
I personally like Fenders and Epiphones, as well as Gibsons and Ibanez'es, to mention a few. The Agile's are a real value and great guitars, but there is also a lot to be said about going to stores and trying out various Fenders, Epiphones, Gretches, etc., until you find one that sounds and feels just right for you and what you think you need. If you are like a lot of us you will wind up buying other electric guitars later anyway, to get other specific sounds and different feeling guitars, tones, and vibes.
One thing that can really throw you off track is going for a specific color guitar, because the one in the color you are looking for might not sound or feel as good as another one in a different color. With this in mind, the sound and feel of the guitar might make the most sense to put your weight on, rather than color or styles of the guitar. I think it takes a lot of trial and error to find the right guitar. A lot of people are still looking for that "right guitar". To many it is the quest, not the destination, that is half the fun. Plus as your playing gets better and your ears get better, you may find yourself reaching for a different type of guitar sound, feel, or look; even a differnet completely different amp. A lot of people start out with inexpensive solid state amps and then progress to more expensive tube amps.
Today there are a lot of great inexpensive tube amps available for a player needing a low power amp; such as the Fender Super Champ XD at fifteen watts and plenty loud, the Fender Blues Junior also fifteen watts but more simple and a great sounding amp; the Bugera V22 twenty'ish watt tube amp combo, the Jet City amps and amp heads and cabinets, the Blackheart amps and heads and cabinets, etc., all costing a reasonable amount. Sometimes you can even find these amps used at excellent prices. One good way of finding out what is a good amp or guitar is to research out what some of the professionals are using, or even local muscians around your area. Professionals and semi-pro's usually have had a lot of trial and error experiences and know what good solid reliable equipment is, that will produce excellent music.
Buying blindly is always a risk and can result in you spending a lot more money in the long run than if you had researched out some really decent equipment to begin with.
I personally started out with a half way decent Schecter super strat but didn't have a decent amp for a while; due in part to resistance from my X wife. My present woman encourages me to only buy real good equipment, instead of spending money on mediocre stuff. I'm upgrading my stuff, but there are many moderately priced guitars and amps out there that would serve you very well. I would say try to stay away from gimicky stuff and odd ball stuff, and go with tried and true products.
I played a real nice Blackstar Venue Series HT Club 40 , no affln., that was a super great amp with enough power for having a lot of fun, expecially if you live somewhere that you can turn the amp up a little, but it works great at low volumes as well. There are plenty of amps that you can spend less money than this on also, of course; and that Fender Super Champ XD is one versitile little amp that packs a great punch and is a tube amp but emulates about eight Fender amps and eight other more high gain amps, plus has some very high quality built in effects, but is not over computerized like a lot of the digital modelling amps. But digital modelling amps are very cool too.
It all comes down to what you really like, and don't be afraid to spend some money. Overbuying a little can give you some growing room, but if budget restraints are all to real, you have to do what you can.
I hope I gave you some decent ideas. There are a lot of other options available and I only mentioned a few decent ones, at least in my opinion. Keep looking and you will definitely find something nice; and good luck. Have fun.