Domain names and hosting are different things. You can buy both from the same provider(usually easier), but don't have to.
Prices for domains are pretty consistent between providers, but there are some that are cheaper than others. Usually there isn't much difference between what's provided.
Different hosts do offer different hosting options, so you do need to know up front what you want, then shop around to see who offers what you need at the best price. There's no point spending on a load of options that you aren't going to need.
Is the site going to need lots of updating, or is it pretty much just the initial set-up and let it be, with the occasional update? Or something more dynamic with regular updates? Either way I can probably help, but the 2nd option will take more work.
I suggest that whatever route you take, let us know on here and we can advise if the option you are going for is a decent one.