While I like and use the Formulary, there is no danger in buying Ilford or Kodak chemistry if it is in powdered form. There are plenty of dealers (Freestyle and B&H come to mind) that do enough black and white business that they go through the liquid chemicals pretty quickly, too. Powder is, however, a safer bet as it has a very long shelf life. Ilford's is a little better because some of the ingredients are segregated from each other; it's a little more work to mix but not that big of a bother.
Here is what I would recommend to a beginner:
Film developer: Kodak D-76 or Ilford ID-11 (more or less identical) - I like Rodinal but it is grainier than many developers and is best used on slow films, or large formats. (One advantage of Rodinal by the way: even though it's a liquid, it lasts for years.)
Paper developer: There are many but the most common is Kodak Dektol. It is an excellent developer. A very good substitute (and preferable to me) is Ilford Bromophen. It is somewhat harder to find but works much the same way. It uses Phenidone instead of metol so it is a little friendlier to the skin (metol can cause allergic reactions in some people.) Functionally it is very similar to Dektol. It also comes in metric measurements which I prefer, and dilutes 1:3 for normal use versus 1:2 for Dektol (although some use Dektol 1:3 and extend development). I recommend that you try both and use the one that you prefer. Some will recommend a liquid concentrate such as Ilford Multigrade, which is a good chemical, but powders are less expensive (you don't pay to ship the water) and last longer when stored (you can keep powders for years; liquid concentrate is good for a year or two at most, and usually less once opened).
Stop bath: Any. I have traditionally used Kodak's which is acetic acid and smells like vinegar (vinegar is dilute acetic acid, so it doesn't smell like vinegar, it more or less is hyper-strong vinegar.
) Ilford's uses citric acid so it doesn't create as much working solution for a given volume of stock solution, but it is also a lot easier on the nose. I use a one-minute running water wash on film but I still use a stop bath with paper.
Fixer: Let's keep it simple. Use an ammonium thiosulfate rapid fixer. These almost universally come as liquids. Powdered fixers are almost always sodium thiosulfate. Ilford's rapid fix is good and it is what I usually use for paper. Kodak's is also good but it comes in US measurements and since I mix in metric, I always end up with weird amounts left at the end, so I use the Ilford instead. Operationally they are almost identical.
If you are printing on fibre paper, you will want to use a wash aid or hypo clearing agent. Kodak's is fine and comes as a powder. Ilford's comes as a liquid so it has a shelf life, but the stock solution lasts longer than the Kodak stock solution after you mix it from powder. Both are good.
Once you've been doing this awhile I would have different answers for you, but it is hard to go wrong with these chemicals as a starting point.
