Speaking as a 6 month old beginner, not necessarily in any order:
A good variable 2x72 grinder is the core of the shop. Having a grinder that will do everything you need it to do is just beyond words. I picked up an Esteem from Brett M and never looked back. I love it. I picked up a 14 inch wheel and am please with it, although I've not been interested in hollow grinding to a great extent yet. I may have jumped the gun on that one but an waiting to see if I get more interested in it. Think through upgrades. It is probably best to just get the basic flat grind down before you venture off.
Quality dial calipers. I love the convenience of digital calipers for quick and easy conversion from mm/inches/fractions, but I have both types.
A good quality drill press. I picked up an old Craftsman 100 and 150 and put in new bearings (quality) and belts, and got them pretty much free except for my labor by parting out things I didn't need on them.(Craigslist). Figure out how you want to clamp your work down for drilling. This is a must for safety. Could be a cross-slide vise which is what I use, or 123 blocks or both.
Carbide file guides. These will save you a ton of frustration on the grinder. I have a pile of scrap blades because I overshot the plunge learning to grind. Having the guides helps you focus on other issues while learning to grind. When mine wear out I will be getting another set, no question about it.
Some kind of machinist blocks for getting a work rest square. I don't use a rest for grinding bevels, but I do use it to profile the shape initially. Having it square is important.
A good carbide scribe with height adjustment. I went with the cheap block scribe to start with and while it is usable and helpful, the height adjustable scribe is quicker to use and easier to be precise with. (eBay).
A portable band saw with a table to mount it to. You can get a Swag table, but I just built my own from oak and metal. I started with an angle grinder, and it's just not a pleasure to use to cut out a blade. One skip across the surface in the wrong place and you trashed the blade. I have a porter cable porta-band and it works great. It's old, but American made and will probably last me through my knife making career. They can be had for 150 to 200 off Craigslist.
A good magnet to hold the blade against to grinder helps when surface grinding. I used to also use it for bevel grinding to give more to hold onto, but have since learned you can just hold it by hand and do very well. It's just a matter of finesse and it will come with practice.
A surface plate (which I have yet to get) can help with scribing, and some types of sanding.
Build a good knife sanding vise or clamp. Nick Wheelers hand sanding videos show this contraption which is just angle iron bolted or welded together. I built one and love it.
A wood band saw for cutting handle scales. You can get away maybe using the portable band saw for a while, but having a dedicated wood saw is nice.
Good lighting. This can make a huge difference at the grinder and for hand sanding. Very important.
Dust collection and respirator.
Craigslist and ebay have been great for providing good deals on these items for me. I buy and sell a lot so it was easy for me to get my stuff. I've also picked up quite a bit of stuff at garage sales for next to nothing compared to retail.
I hope this info is helpful.
Thanks for such a detailed response! Lots of good info in there