Yup. I have most of the stuff everyone has mentioned, but I started with a 25' roll of 24g kanthal, a pair of old needle nose pliers and a sharpie. I made several twisted coils by looping a length of wire around the marker and twisting the ends with the pliers.
There are a few things you can do without a drill but if you decide you enjoy tinkering it won't be long before you want a drill.
Here's what I would suggest for initial purchases. I'll start with the stuff you can get at Harbor Freight.
Inexpensive cordless. Either from Walmart or Harbor Freight, $20 will do it.
A trigger clamp.
With this you can forgo the need for a vise. You will most likely need to drill a hole in the bar so that your swivels are in line with your drills chuck. As luck would have it you just happen to have a drill handy to do the job.

I have a smaller trigger clamp for when I want to go ultra portable, but the clamping force from the bigger one (the one in the pic) offers the stability you'll want for doing complex builds. I have a couple of vises, but I always come back to the clamp since it's so versatile.
Flush cutters. Buy a few of these while you're at HF. Generally I consider flush cutters disposable. They are pretty delicate. You can make them last using proper technique, but even $50 (a pair) Lindstrom cutters are sold in packs of 3 (or 5?) because they won't last forever. Outside of HF there are many options, but the super cheap HF cutters are great. I just bought some decent Xuron's (

made) at Hobby Lobby and they are fine. After the ubiquitous 40% off coupon I think they were around $10. At Home Depot you'll find a Cresent brand kit that includes a very nice needle nose pliers and flush cutters. I love the handles and HD has been good about replacing the cutters after they get chewed up. I think the set is around $15
Lots of other odds and ends at HF, but a drill, clamp and pliers/cutters is a good start.
Spool Tamers. Absolute necessity for me. You can buy them online or at Hobby Lobby. HL sells 3 packs for a great price. I suggest you buy 1 for every spool of wire. You can auto clapton with just a single tamer.
Wire. Duh. Just buy a variety pack at kbee for next to nothing. I suggest the pack that has spools in 24, 26, 28g and 30g along with a pack of wrap wire in 36g from their wholesale page. If you have the $ throw in a 50' spool of ribbon wire.
Swivels. I love the Japanese made Spro Heavy Duty ones. Size 5 are rated to 560lbs and aren't so heavy that they pull on your wire like others can.
I think that's enough to get you started. You can make pretty much anything with the above. There really aren't many specialty tools needed and you can piece-meal all of that together as you go. For instance, you may find that you require a good lighting setup, or magnification considerations. A wire crimper for doing corrugated builds... Stuff like that. To get started though the buy in isn't so bad.
Drill $20
Wire $30 (for a LOT)
Clamp $4
Swivels $15
Pliers/cutters $15
Spool tamers $6
Just a rough estimate but you shouldn't have any problem getting started for under $100. That's all in with supplies AND tools, it's gotta be the least expensive hobby I've ever had. Then again I've definitely got over a grand spent now and probably closer to 2k but that's a personal problem, not the fault of the hobby!
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