Bryan, if you can read a list of instructions and pour water from a kettle into a mug, you can pretty much process black and white film.
It's been said over and over by me, but the single best thing I've been recommended on here was
the fantastic ilford guide to processing your own B&W film.
Really, it IS as simple as following that list of instructions.
For Black and White, as a starter kit of chemicals, I'd go for these...
Developer -
Ilfosol 3 (keeps fairly well, easy to mix liquid dev.)
Stop Bath -
Ilfostop
Fix -
Ilford Rapid Fix
Wetting Agent -
Ilfotol (only needed if you live in a very hard water area - i'd try without first and only get some if you have problems with drying marks on the neg's)
The Developer is a "one shot" - mix it, use it, throw it away, the fix and stop are re-useable and last for yonks. Make up a litre at a time and store it in 1L plastic milk bottles, clearly labeled of course.
All chemicals are from same ebay source... I've used the guy, and he's happy to combine postage - all 4 would normally come in at the single £5.50 - wet chemicals theoretically need to be sent via a courier rather than parcel-post. You may be able to source somewhere cheaper, but ebay was a nice easy place to get pictures and descriptions
As to hardware, well it's really down to
Processing Tank -
Patterson Universal is a good one - can take 2x35mm (with additional spiral) or 120/620 film
Measuring Cylinders - a smaller grad for measuring the chemicals and a larger one for the overall volume of liquid are handy, say a
45mm and a
300ml plus 4 or 5 1 litre plastic measuring jugs from asda at 50p each.
Thermometer - processing is pretty temperature sensitive, and a
thermometer is a good idea from a point of view of consistency.
Changing Bag - unless you've already got a completely blacked out room, a
changing bag is a good idea for loading film into the developing tank. Can't recommend any specific one of those - but my recomendation is to get a big one - especially if you've larger hands, and preferably not made of nylon (as they get full of static, and end up charging the film so it holds every bit of dust in the entire room!)
Negative Sleeves - yep - you'll need
something to put the film in after it's processed, otherwise it'll start attracting dust again. Dust will be the bane of your life when you start scanning film, so be prepared.
the rest of the kit list from the ilford howto, you'll probably have lying around the house, or be able to pick up on the highstreet/improvise somehow.