Calipers - I know I'm going against what a lot of guys here will say but I prefer digital over dial calipers. At work I train customers all the time on how to properly use the hydraulic hose crimpers that my company makes, and a big part of that is double checking the results with a set of calipers. Even a $15 set of digital calipers from Lowes is plenty accurate for reloading, and much much easier to read. I've seen a lot of people misread dial calipers, which really aren't that tough to read (try teaching someone how to read a vernier caliper). The only downside to digital is that batteries die. I have two sets of calipers, one digital, and a backup dial for when the digital batteries are dead.
For a tumbler, the best advice I can give is to get one with a solid lid. A lot of them have "separator lids" which you can use to sift the media out of the cases when they are done, but I've always found trying to separate the media like that was clumsy and awkward. The big problem with the separator type lids is that they let all of the dust generated by tumbling escape into the air and get all over everything. That dust can contain lead from the primer residue, so it's not something you want to be breathing in or spreading around your house. I use a solid lid, and throw 1 or 2 used fabric softener sheets in with the cases and media, they work really well for trapping most that dust and grime, which helps the media last longer as well. This looks like a good setup, for the same price as just the tumbler from the other brands: http://www.midwayusa.com/viewProduct/default.aspx?productNumber=414369
You said you planned on using walnut media, which will work fine. It leaves a rougher finish on the cases, but cleans quickly. I use corn cob media (you can buy ground corn cob from pet stores or feed co-ops much cheaper than gun stores/sites usually, pet stores sell it as rodent bedding) mixed with some RCBS polishing compound: http://www.midwayusa.com/viewproduct/?productnumber=135675
All the other case polishes I know of are liquids, and I found that the dirt and powder residue from the cases stuck to and coated the damp media fairly quickly, making it much less effective. The RCBS powder lets the residue escape as dust, keeping the media cleaner and letting it last much longer. Just add a new packet of polishing compound every so often.
Case trimmer - if your kit doesn't already have one, I have a Lee hand trimmer that works just fine and was cheap. It can also be tightened in a power drill for use as a power trimmer if you have a lot of cases to trim. You'll need the case holder and cutting blade which works for all calibers http://www.midwayusa.com/viewproduct/?productnumber=476992 , and then a length gauge and shell holder for each caliber you reload, for example here's the one for .223Rem http://www.midwayusa.com/viewproduct/?productnumber=107333 Remember to get a chamfer tool. Even if you aren't trimming your cases, a little bit of a chamfer will make seating the bullets much easier, and new cases always have burrs at the mouth and sometimes even the primer pocket that need to be removed. http://www.midwayusa.com/viewproduct/?productnumber=389104
Dies - I have some Lee dies and some RCBS, they both work well. I prefer Lee dies for straight-walled handgun cartridges, and I like RCBS for rifle. Make sure to get carbide dies for your handgun cartridges if you can. Carbide dies don't require lubrication when sizing your cases, steel dies do. Imperial Sizing Wax is great stuff for that. If you try to size a case in a steel die with no lube, it will get stuck and you'll spend a lot of time trying to get it out.
Also, the type of rifle dies you buy depends a little bit on what they'll be used in. A full-length sizing die should be used on all brand new cases, ammo for semi-auto rifles, or ammo that might be used in more than one rifle. If the ammo will only ever be used in one specific (non semi-auto) rifle, and your empty brass was all fired in that rifle, then a neck-sizing die is all that is needed. It only re-sizes the neck of the case so the bullet is held correctly, leaving the main body of the cartridge in the shape created when it was fired in the chamber. Basically the cartridge case is a custom fit for that gun only which can improve accuracy, but it may or may not feed in other guns.
When you buy your dies, also buy an extra depriming (decapping) pin for each set. Nothing is more frustrating than breaking the depriming pin on your sizing die and realizing your reloading is over until you get a new one, especially if you have to wait for it to be shipped to you. Midway has an entire section devoted to them: http://www.midwayusa.com/browse/BrowseProducts.aspx?pageNum=1&tabId=1&categoryId=19924&categoryString=9315***731***702***9169***
Hand Priming tools are nice, but not a necessity. I have a Lee and it works great, but I still do a lot of priming on the single-stage press.
Bullet puller - I will fourth the recommendation for one of these, a simple hammer-type impact puller will work just fine for now. In the beginning you should be double and triple-checking your rounds at every step, so the chances of winding up with 100 or more rounds to be disassembled should be very slim. I've gotten by with just an impact puller for 3 years now.
Reloading blocks - As also said before, pick up a couple more of these, they're always handy.
Latex or vinyl gloves - I got into the habit of wearing surgical style gloves when reloading because my hands would get filthy, especially when handling fired cases, tumbling media, plain lead bullets, or lubing and sizing rifle cases. With fired cases and tumbling media, the dust and residue can contain lead because most primers still use lead in the explosive compounds. They aren't a necessity, but anything you can do to help limit your lead exposure is probably a good idea.
Ammo boxes and labels - You are going to need somewhere to put your finished ammo, and you will want to keep track of batches including things like type/weight of bullet, type of brass, type of primer, powder type and charge, and even the number of times the brass has been loaded, so that you can compare accuracy of different loads. The Frankford Arsenal plastic ammo boxes work great, and self-stick printer address labels from Wal-mart stick well to them.
Storage bags - I use a lot of bags to keep my components organized, especially bulk brass and bullets. It seems like everything I order comes in bulk boxes and once I open them it gets difficult to keep things clean and separated. Cardboard boxes have a habit of tipping over or falling off the shelf when they're around me, spilling whatever is inside. www.grainger.com is a great source for bags, plastic bins, or whatever you need to keep your area clean and organized. They sell bags that are much thicker and stronger than regular zip-loc bags, which is important when you're using them to hold things like brass cases with sharp edges and heavy, pointy lead bullets. I like these plastic bags: http://www.grainger.com/Grainger/Seal-Top-Poly-Bags-2EWR2?Pid=search
And these cloth bags are handy as well: http://www.grainger.com/Grainger/MIDWEST-PACIFIC-Drawstring-Parts-Bag-5DJA4?Pid=search
Books - I taught myself to reload with just the Lee manual http://www.midwayusa.com/viewproduct/?productnumber=484416
I wouldn't recommend using just a single manual to anyone else though. I think that it's never a bad idea to have several different manuals so that if you get confused with part of one manual, you can compare it to the others. The Lee manual has a lot of good information in it, and a lot of load data for all different cartridges. You already have a couple good manuals ordered, but think about picking this one up too. Lee does have parts where he seems to be focused on selling his brand of equipment more than explaining how to reload properly, but overall I found it very straightforward and easy to understand. In combination with this forum, I was able to learn how to reload despite not having anyone to help me in person.
Get some safety glasses, and wear them. Even the act of seating a primer just like you've done a thousand times before can be enough to set it off, and if little pieces of shrapnel from the primer or something around it start flying, your eye is the last place you want them.
I know that was a lot, I hope it wasn't too much. Reloading is really a simple, straightforward process once you get into it. There are definitely some dangers involved but they can be avoided if you learn to do it the right way in the beginning. Then you'll end up with a great new hobby and ammunition that performs better than anything you can buy.
