To set the record straight, there are only eight Ivy League schools. They are:
Harvard
Princeton
Yale
Brown
Cornell
Dartmouth
UPenn
Columbia
MIT, Stanford, CalTech, and UC-schools are NOT Ivy League schools, although they are certainly all fine institutions, and may for some subjects have stronger programs than Ivies. Bear in mind that the Ivy League wasn't originally about academics. The eight Ivies were in a football (American) league together, and played against each other. All are academically excellent, but there are many schools that are not Ivies that are great too. All the Ivy league schools are private, meaning the cost of attending them is very high. Also bear in mind that the cost of education in the US is much higher than in England. For room, board, and tuition at most Ivies, the price tag for a year is usually at least $38,000.
In terms of good public schools, the prices are lower to a degree, but you will not be eligible for in-state tuition, which is where you really find bargains. UVA and William and Mary in Virginia are great public schools. So are UCLA and UCBerkeley. UMichigan has a very strong reputation. Take a look at those if you're applying in the US.
On essays, it's worth looking at some US websites on American college essays. They are dramatically different from the PS English students are used to.
Mostly, there isn't a good corollary to UCAS here. You can use the common application to apply for a lot of schools, but some schools don't accept the common app, and most good schools require supplements.
Anyway, hope all of this helps. Feel free to e-mail me with questions--I've done a good amount of looking at this system for the last four years.