Black and white film development can be daunting to beginners, and while it does require a bunch of tools and new items, the actual process is not any more difficult than baking bread. Further black and white film is enormously flexible and while you can really dial in the process to get precisely the results you want, even with a lot of variation you're likely to get useable results. As an example I once accidently cut my dilution of HC-110 in half and, while my film was very thin, I was still able to scan usable images.
there are lots and lots of developers out there. HC-110 is a great choice for beginners. It’s a liquid concentrate easy to mix up for each development, lasts for ages, and produces good consistent results. Rodinal is another classic choice, is cheaper, but produces a pronounced grain which is less universally liked.
A small assortment is nice. 10ml-100ml not a big deal. I think I got a a couple sets of glass ones one amazon.
Some clips to hang film with
Process
Before hand
Mix stop and fix.
The appropriate dilution will be listed on the bottle. These chemicals will be reused across a number of development cycles. They should be labled and stored as airtight as possible, in a cool, dark location. I use 1L amber bottles listed above.
Both stop and fix will eventually expire. The Ilford stop bath listed above will start yellow and turn purpleish when it's expired. When the stop is expired you can simply pour it down the drain and make more. The fix is a little trickier. It will last quite a while, I usually just watch for an increase in film base fog. When I see my film come out a little grey, I mix some new fix and just refix my film. Fix should NOT be poured down the drain, I take mine to a locally community film lab that processes the fix to remove the silver.
Mix your developer
Specific directions will depend on what developer you're using. If you're using HC-110 like suggested above then you need to pick a dilution. I like 1+63. For a two roll paterson tank you need 500ml of developer meaning you should mix 8ml of developer with 492ml of distilled water.
Set a timer
Massive dev chart is the standard starting point. They make an app with a timer that is cheap and I like. For HP5+ rated at 400 and HC-110 at 1+63 the suggested dev time is 11 minutes.
Get all chemicals and rinse to temp
I like to use a sous vide. It's not the fastest method but it is absolutely mindless. I just put all the bottles in the tub with water covering them and set the sous vide to 68 degrees.
Transfer the film onto the paterson spools
Can be trickier than it sounds. Lots of good youtube videos on it. Can be nice to practice with a trash roll in the light. This is the only step that needs the dark bag. Put your roll in the dark bag with the tank and the tank bits (spool, tube, funnel, etc).
Prep all your bottles and timer and make sure you’re ready. Double check time and dilutions.
Development
Dev (check massive dev chart)
Add dev to tank
Start your timer
Agitate: Gentle inversions for the first minute, then two inversions every 30 seconds
Pour down drain
Stop (1min)
Add stop to tank
Agitate: Gentle inversions for 1 minute
Return to stop bottle
fix (5min)
Add fix to tank
Agitate: Gentle inversions for the first minute, then two inversions every 30 seconds
Return to fix bottle
Rinse (2min)
Add water to tank
Agitate: Gentle inversions for 1 minute
pour out and replace water
Agitate: Gentle inversions for 1 minute
Wash (5min)
Open tank, remove funnel, let sink run gentely into the tank for the full time
Photo-flo (1min)
Fill tank to top of spool with distilled water
Add 1ml of photo-flo
Agitate: Gentle inversions for 1 minute
Hang to dry
Final thoughts
This is only a starting point, as you'll discover there are endless variations on this process and this is just one that works for me. Some places to explore if you want to do some adventuring would be to play with different film and developer combinations (Other good developers to try would be Rodinal, Xtol, and D76). Another avenue would be to research the zone development process for contrast expansion and contraction as well as film testing. But mostly this is presented as a way to get your feet wet and start to get some results.