Well, as far as building goes, it depends if you want to build an ARF (Almost Ready to Fly) or Kit-type plane. Kits require more tools. ARF's are more expensive. If you're going for total economy, you can build more kits cheaper by making an investment in tools, but it also takes more time.
ARF suggestions = sheet or two of sandpaper, 200-ish grit's fine for what you'll be doing. Phillips and Flat-Tip screwdrivers (I recommend 3 sizes of each, you don't need the 'manhandlers', just small to about a #2 phillips is just fine). You need glue. Get a few bottles of the stuff. CA, and though people have their favorite brands, I only suggest the kind sold in model shops. Get one bottle thick and one bottle thin. 2oz each should build a couple of ARFs. Get some epoxy (whatever the ARF maker recommends). You're going to need some. You can mix this stuff on coffee-can lids with toothpicks. Little investment there. I've always loved having a razor-saw and a saw box, but that's more a kit builder's necessity. I've used it on ARF's, though to help finalize radio installation.
Don't be afraid to get a modeling (X-Acto) knife you like with spare blades. Sharp is a good thing.
It's not equipment per se, but a nice flat table-top you don't care about is a good thing. Something you can paint, stab into with drill-bits etc. Speaking of drill bits, you'll find it pretty hard to complete a plane that needs drilling without them. An inexpensive set of chinese drill bits is all you need (you're not boring through nickel ingots here).
If you're kit building, you'll also need a heat gun, heat iron (for afixing monocote), jigs, clamps, more sandpaper (more grades), potentially a wire-bending jig (for models without pre-bent landing gear), more drill bits (because you'll potentially be drilling larger holes, ARF's tend to need only small ones).

Put the screwdrivers, one knife, a locking set of pliers (million and one uses), and a good set of allen-head (hex) keys in your field box. Also, I built a caddy for glue and I always keep spare screws, control horns etc in the box. Not a bad idea to keep some 1/4 x 1/2 balsa stock (works great for repairing crash damage @ the field).

Someone else will certainly say you need more. You probably do, I'm certainly forgetting something

As far as your engine goes, if you want to go budget, all you really need is a glo starter (you pick which you want based on price / convenience), fuel and a chicken stick (assuming your engine's ready to go with plug installed). I always keep a glo-plug sized wrench. I have a cheep russian socket set that fits everything and cost me $19 at a hardware store. You'll need something for your prop nut and something that fits your spinner, if you have one. You can go full-blown with electric fuel pump, electric starter, gel-cell start battery, glow driver, field charger, power panel and a fully decked-out box.

NO. Not everyone does this, even the ones with all the money they could want and years in the field. I see plenty of people gravity-siphon filing their tanks, who start with chicken sticks. Have someone experienced show you how to do this. Note, bigger engines often REQUIRE hand starting... Check @ your local field.

Believe it or not you can get out of the hobby shop after spending about $200 with pretty much everything you're going to NEED. Or, you can do what I did and spend $500 and not even get what you wanted. LOL. I've found out through use that I could have left some @ home.