Welcome to the forum, and how exciting to be looking to get your first horse!
Horses need to eat 1-2% of their bodyweight in feed per day, and at least half of that should be hay or pasture to keep their gut in good order. However in some places, such as here in Australia, pasture hay and grass has very low nutritional value due to the nature of our soil, so I also feed (or fed, while I was setting my horse's feed plan) mineral supplements, alfalfa and oaten chaff, rice bran and oil. He couldn't get by on just grass, even if he was getting more than enough (such as in the wet autumn we just had) it wouldn't be ticking all the nutrition boxes. So it is quite dependent on the quality of the pasture, the number of acres per animal and weather.
Another thing to consider is the horse itself. Some horses are "good keepers", some horses are "hard keepers". Thoroughbreds are generally hard keepers, ponies good keepers, but this isn't a hard and fast rule and they all still need minerals such as calcium and magnesium to keep them in working order.
Thirdly, it matters how much work you plan to have him do and what type. Most of us don't really go past light-medium work, but if he's going to be competing cross-country, for example, he will need a higher-energy diet than if he's taken out for a hack a few times a week.
I strongly recommend that you check the place out before you consider sending your (soon-to-be) horse there. Look at the condition of the animals. Are they ribby or well-fed? Do their hooves look in good condition? Do they bear a lot of pasture scars (might be overcrowded contributing to more fighting, or fencing may not be safe)? Do their coats look healthy? Does the place generally seem professional?
Most decent agistment places offer feeding services (for extra charge) and will do 2 feeds a day (morning and evening). They may also do rugging, organise the farrier and dentist visits, and do worming and vaccinations. I would seriously consider getting third party/public liability insurance to protect you in case your horse breaks a fence or hurts someone - it doesn't usually cost very much (mine costs $140 a year) and is very handy to have.
And wherever you go, make sure you have a contract that clearly states the conditions of the agistment! We've had some horror stories on here from people who didn't have contracts (some ended happily but it's not always the case).
Best of luck in the hunt for your horse, and his/her new home!