That'll be a long list, but here goes nothing:
1. An up to date reloading manual from your favorite bullet manufacturer. This is always the best place to start.
2. Single stage press. I started with an RCBS Rock Chucker, and I'd recommend it to anyone who wants to start reloading.
3. Hand priming tool. I'm an RCBS fan, and I like theirs, because it uses the same shell plate as the press. No need to buy extra shell plates, if you don't want to.
4. RCBS M500 Mechanical Scale. Not as nice as the old 5-0-2, but it works just fine.
5. Lee Improved Powder Measure Kit. I don't use a trickler, when I'm hand-weighing every load. I just pick the appropriate size scoop and meter the powder out of it directly into the scale. I'm sure there's a better way to do it, but I've been doing it this way for years, and it works.
6. Lee Powder funnel, 22-45 caliber. Cheap plastic funnel. It works better than the RCBS one.
7. Chamfer/Deburring tool. Both the L.E. Wilson and RCBS ones are nice. Both tools in one piece.
8. Shell holders and Die set(s) of your choice. I'm a big fan of RCBS Full-Length Die sets. Start with the Full Length Die set, and add the neck only sizing die later on, as you get more serious about dialing in the accuracy of your bolt guns.
9. Good quality Digital Micrometer. Available at any reputable hardware/tool shop. Essential for checking case length and getting bullets seated to the right depth.
10. Impact bullet puller. I have the National Metallic one from Midwayusa, and I like it. Mistakes will happen. These are used to disassemble loaded ammo, so you can reuse components.
11. Hornady one-shot case lube. It should actually be called 2 or 3 shot, but it goes on easy, with no lube pad required. Wipes off easily, too.
----All of the above equipment should get you going with new brass or fired brass that's already been prepped. Once you have a stockpile of used brass you'll need a couple more things to prep them for reloading-----
12. Case tumbler - I wet tumble my brass. I really like the Dual Drum Rock Tumbler from Harbor Freight. It's perfect for small batches of brass - you just need one pound of stainless steel media for each drum. You'll also need a few accessories to go with it. I have a couple 3 gallon buckets and a cheap plastic pasta strainer I got from the local dollar store. They make it easy to separate brass and media. The Frankford Arsenal Media Transfer Magnet makes short work of picking up stray media.
13. Case Trimmer. I use a Lyman Universal Trimmer. It works OK, as long as you do small batches. This is something I'm looking to upgrade in the near future.

There it is. That's my best attempt at a comprehensive list. I'm sure I forgot something, but I think that should be all you need to get going. Good luck and, like I said, Start by reading the manual!