Great question TJ. I'm no honemeister, but there are a couple of avenues you can take IRT getting started in the honing world. You first need to decide whether you want to go natural or synthetic, or a combination there of. I personally use synthetics to set my bevels, and a JNAT working through different Mikawa Naguras (slurry stones) to refine my edges. I've had pretty good success with this, though I really don't have much to compare to. Eventually I'm going to send one of my razors out to Alfredo in the littlest state to have a professional JNAT edge put on and see how I'm shaping up.
I started out, however, using an inexpensive King 1k stone for bevels and lapping film for refinement and finishing. I had mixed results with this, and ended up investing in some better synthetic stones for the bevel setting and some initial edge refinement, in the Shapton Professional 1.5k and 4k stones. If you want what many consider to be the top tier bevel setting stone, look to the Chosera 1k. Eric (Smattayu) would be a great person to speak with on the lapping film, as he's had great results with it.
With any stone, you're going to need to get something to lap it flat periodically, so a diamond plate or lapping plate is a necessity. I have a 400 and 1k lapping plate/honing plate for this, but wish that I had spent a little bit more and gone with an Atoma diamond plate instead. Having a flat stone is a prerequisite for getting a properly honed blade, and its importance can't be understated.
Some people have the best luck with a straight synthetic progression of stones. If you decide to go this route, try to stay with the same type of stones. (i.e. Shapton Glass stones from 1k through 16k or whatever you're using as a finisher).
There are others that are all about using a single stone to do everything from bevel setting to finishing on one stone using different thickness slurries. This is typically done on a Belgium Coticule, but it takes some practice to get the single stone honing down. I could do this as well with the JNAT and a full Nagura progression, but it takes a while to set bevels doing that, which is why I have the synths.
Cost wise, Coticules can represent possibly the best value, as you can do all of your honing on that stone. But the trade off is the time you're going to spend on them. JNAT's tend to be more expensive per stone, but you can find good stones and nagura sets for around $200. Typical bench sized JNAT's get very pricey, however, some costing upwards of $1k depending on the mine and vein they come from. A similar sized Coticule can be obtained for 1/3-1/2 the cost, and only requires one slurry stone.
My personal recommendation would be to go with a synthetic progression and a good lapping plate, however. There is no slurry to worry about, and it's generally a straight progression from one stone to the next. Naniwa Super Stones, Shapton Glass Stones, Shapton Professionals are all a good place to start from. A progression would look like this: 1K, 3-4K, 6-8K, 12K. You can stop there, or keep going with the 16k Shapton glass stone, or the pricey 20k Suehiro Gokumyo. There are other stones that can be fit into that progression as well, but for bevel set to finish, four stones should be plenty. You can do further refinement of the blade with a pasted balsa strop and regular stropping. The downside to the synthetics are that many claim they just don't have the "zen" feel that honing with a natural stone does.
If you're just wanting to keep it inexpensive, get a decent bevel setter, (doesn't have to be a Chosera 1k) a lapping plate, and a progression of lapping film. Make sure you have a flat surface to use with the lapping film...a piece of smooth tile or something along those lines. You'll be out a fraction of the cost of going with a full progression of stones, it takes up less room, and again, is pretty straight forward in its use and function. There are people who get edges sharp enough to cut through time with lapping film, so it definitely works. They might not be the most forgiving of edges, however.
In the end, it's all what you're looking to get out of it. If you're just looking for a finishing stone, there are plenty of options out there that I didn't touch on such as Arkansas stones, Thuringian (thuri's), etc...because I have zero experience with them. Hope this helps!
