Since you are a rookie to both driving and turning wrenches, and probably have a shoestring budget, the FWD car will be a fine place to start. Although the FWD car won't drive like a Late Model, nothing except a Late Model drives like a Late Model. What you need starting out is to learn how to race. If you have some talent and perseverance you will be able to adapt to different cars as you move up.
Like most racing classes, the costs can be as much or as little as you decide to invest. (You can substitute your own labor for some costs.) Make a list of work you need to farm out (such as installing a roll cage) and then ask car builders in your area what they charge… better yet, build a team of people who can do these things and instead of paying retail you might get away with a few meals and cases of beer. I suspect that you can get a FWD car onto the track for a few thousand dollars, and only spend about a hundred per week supporting it (if you don’t break)… try asking guys already racing in the FWD class what they spend. They may not be fully forthcoming, but you should be able to find the ballpark.
Basic tools: floor jack, jack stands with plates welded to the bottom (so their legs don’t sink into soft pit dirt), safety gas can, 4-way tire iron (paint the correct sized end so you know which one it is quickly), box of typical hand tools, auto test light, funnels (one for fuel, one for radiator), bailing wire, duct tape, pry bars of various sizes, heavy hammer, battery powered drill with bits, pop rivet gun with rivets, tape measure, air tank, tire pressure gauge, tire tread depth gauge, crayon that can write on tires, grease gun (if your car has grease fittings), rags. While building your car you may find that you need a special tool or to modify a tool – keep track of those.
Spare parts: extra fuses, extra (already mounted) tires, extra lug nuts, battery, oil, radiator fluid, brake fluid, brake cleaner, transmission fluid. Some cars are notorious for breaking certain parts, so if yours is prone to that (and it can be changed at the track in time to make the race) stock a few of those. Don’t forget a spare tire for the trailer.
I’ve probably forgotten something, so watch other crews to see what they use. There are some good books on racing FWD cars – look for one for racing on dirt. Circle Track magazine had some good articles (before it went under) – you might still find them archived on the Hot Rod web site. Please consider if budget limits force you to cut corners, don’t cut corners on safety gear. Best of luck!