I recommend you get a book on darkroom basics, such as
The Basic Darkroom Book, 3rd Edition by Tom Grimm -- or browse a local book store or library. Alternatively, read a few Web sites, such as
The Black & White Darkroom. That said....
Briefly, you need at least two chemicals (three if you count water) to process either B&W film or B&W paper. Others are optional:
- Water pre-wet -- optional, used mostly with film.
- Developer -- develops an image. This one is mandatory.
- Stop bath -- a mild acid solution (less acidic than vinegar) that stops development. May be skipped or, more commonly, a short water wash may be substituted.
- Fixer -- removes undeveloped silver halides from the emulsion, making the image permanent. Mandatory.
- Hypo clear -- speeds the following wash step, but how much depends on the fixer used. Often skipped for some types of paper and even with film when using certain fixers.
- Wash -- a water wash of 2-40 minutes, depending on materials and whether or not hypo clear was used. In this context, "wash" means to leave the film or paper in running water; there's no soap involved!
- Wetting agent -- optional and used only with film, this final step makes the water more slippery so that it slides off the film without leaving drying marks.
As to specific products, there are many choices, and unless you get into really exotic stuff, it's hard to go badly wrong. For developers, common beginning products for film include Kodak D-76, Ilford ID-11 (which is almost identical to D-76), Kodak XTOL, and Kodak HC-110; but there are many other possibilities. For paper, Kodak Dektol is the standard beginning developer, but lots of others will work as well. I like a mix-it-yourself developer called DS-14, which is related to a commercial one called Silvergrain Tektol.
For stop bath, I'd get any indicator stop bath. This contains a dye that changes color as the pH changes, which will tell you when the product is too old to be used any more. (You can re-use indicator stop bath.)
For fixer, just about anything will work, but rapid fixers work more rapidly than non-rapid fixers; however, rapid fixers are made from an ammonium compound, and so some of them have a strong ammonia odor. Just how strong varies depending on other factors. Kodak Flexicolor fixer, although marketed for color film, works with B&W film and paper and is inexpensive; or you could buy TF-4, which is more expensive but has clearer instructions for use with B&W products. TF-4 is one of the fixers that benefits least (maybe not at all) from a hypo clear product.
For hypo clear, I have no strong recommendations. For a wetting agent, Kodak Photo Flo is the standard, but Ilford and others make equivalents. I know of no reason to favor one over another.
Now, on to paper....
B&W papers vary in two important dimensions: base (fiber-based [FB] or resin coated [RC]) and contrast control (graded vs. variable contrast [VC]; VC is also known as multigrade [MG] or other similar terms). For beginning work, a variable contrast fiber-based (VC FB) paper is best. The VC characteristic enables you to change the contrast of a print via filters (which may be built into your enlarger or can be bought separately). Graded papers, OTOH, require you to change papers to change contrast. The VC feature is therefore very helpful when learning, since you don't need to keep multiple stacks of different papers on hand and you can experiment with contrast quite easily. In terms of FB vs. RC, FB is the traditional method of making photographic papers. RC adds a resin coating to the paper that tends to reduce wash times and make papers dry flatter (or with a uniform curvature), vs. the wrinkled sort of way that FB papers tend to dry. RC papers are also stiffer when wet; FB papers tend to flop around a lot. Thus, RC papers are easier to handle in the darkroom and produce flat prints with little fuss. OTOH, some people prefer the look of FB papers; but IMHO, for learning purposes RC papers are superior.
Within the VC RC realm, there are lots of choices, and every single product on the market has its fans. Since I don't know, and even you probably don't know, what your preferences are/will be, my recommendation is to buy whatever is inexpensive and/or easy to obtain. Once you've used a couple of 100-sheet boxes, you might want to try other products for comparison. Ilford is the big name in the field, while Foma products are probably the least expensive (but may be hard to find locally). Adox, Kentmere, Oriental, and others are also available.
Sometimes manufacturers make similar papers that vary in tone. This is the color of the paper -- cool tone papers tend to be slightly blue or green, whereas warm tone papers tend to be slightly brown or red, and neutral tone papers have little color tone. These effects are fairly subtle; we're not talking about a flaming sunset red or sky blue here, just a very subtle color effect that you might not even consciously notice except in a side-by-side comparison. Warm tone papers are often preferred for portraits or other subjects in which you want to draw the viewer in emotionally; cool tone papers are often preferred for emotionally harsher or distant subjects (say, industrial architecture).