Rayong is not that far from Bangkok, maybe an hour drive by taxi since the Bankok airport (Suvanabhumi) is outside town on the east and Rayong is to the Southeast.
If you are flying in from the US you will almost certainly fly into Bangkok and take a taxi from there since flying that short a distance wouldn't make sense and you won't find international flights into that other airport. Taxi fare is inexpensive in Thailand so an hour drive by taxi makes a lot more sense here than in america, but I'd just be guessing about the cost (maybe $30).
To find hotels the Agoda site is usually best and easiest to use. You can sometimes find better deals through other sites (eg. booking.com), or possbily can do slightly better directly through the hotel, but usually Agoda is either best or almost the same, even though quoted prices don't include 10% service and 7 % tax additions (which they specify). Local travel agents here can sometimes do slightly better than those options but it definitely wouldn't be worth the marginal savings, and language would be a problem unless you speak Thai.
As far as selecting a decent hotel they use a star system here and usually 3 star and up are ok. 2 star hotels are cheap ($20 / night range) but it's hard to know what the trade-offs might be; musty smell in the rooms, antiquated furnishing, water dripping inside the hotel room. 3 star hotels would seem normal and those prices are usually also low here, $30 to $50 per night.
The 4 star level just increases facilities decorations and ammenities, adding services, a breakfast, pool, better internet connectivity, etc. Some of these might be relevant enough to warrant using a better hotel, but then since Rayong isn't a tourist destination (it's an industrial area) you'll probably be researching to find options that work.