frankly I would avoid a tremolo at any skill level
Hard to avoid one if 80's rock/metal is your thing and many other genres.
OP...one of the main issues a beginning rock guitarist has is his sound doesn't sound like the music he wants to duplicate.
This is usually due to effects pedals/processors.
There are quite a few small amps that have a few of the most popular ones built-in.
They are not going to be as great as some of the legendary studio amps, but they will get the job done better for a budget-conscious student that can decide in a few months/year if upgrading is worth it.
The key thing is to find the guitar type you like which is usually by looking at what your favorite artists use. Stratocaster, Telecaster, and Les Pauls are the most popular. Flying Vs, Ibanez and the like not so far behind.
They all have a unique sound and not all of one type are equal.
Personally I think an Acoustic is the best to learn on...but if you never have a desire to play with one it's ok to go straight to electric (I did in fact and was even able to 'ace' my Classical/Spanish guitars classes at college level when the teacher said I'd probably fail using an electric).
Certain music stores offer money back upgrade plans so look into those too if you think you may be looking to upgrade in a year or two. Sometimes it's better to sell-outright, but sometimes their upgrade plan could be 100% of your purchase price. (YMMV this may have been lost with the economy).
I just bought a Yamaha acoustic/electric 3/4 sized for my 11 year old this christmas...he lost interest mostly and just wants to strum it and do non-music....but it's still fun for him and maybe one day he will dive into a book and start learning theory and playing real songs.