I'm am by no means an expert -- I'm only now just getting back into recording for fun after a ten year hiatus. Fortunately gear has gone up in performance and down in cost radically since I was a wannabe trying to record onto my Pentium Pro with my Soundblaster card. Still a wannabe, but have better gear now.
Now it sounds like your Dad's just doing this for fun, so I'm going to assume a modest budget and time-commitment here. I'm in the same boat with some combination of guitar(s), bass, keyboards, percussion, and vocals depending on who's over.
You'll need at the very least an 8-channel mixer and depending on how serious your Dad is, you can get decent quality recordings with a 4-track recording interface into your computer or laptop. Most of the modern interfaces are USB-based and if you're planning on using a laptop, you'll need that. If
As far as mixer goes, I have a 25-year old Tascam M-308 that serves me well into my (new to me) Delta 44 I just picked up that gives me 4 discrete balanced inputs (and therefore tracks) in Adobe Audition, the software I'm currently using for recording. The Delta 44 is a PCI card that's in my desktop computer in my office (that's conveniently right next to our jam area).
Since we're jamming and there's no dedicated sound guy (or even proper isolation), I've spent some time getting the levels right, marking them with masking tape and making notes, so I can just hit record and not worry about any mics that are too hot, too cold, clipping, etc.
The M-308 allows me to group channels together to sub-outs so that I can combine my 4 drum mics (two left and right overheads, one for snare, one for kick drum) into two tracks (using input 1 and input 2 on the Delta 44). Depending on how many guitar players there are, I either run channel 3 (bass) direct to input 3 on the Delta 44 and channel 4 (guitar) direct to input 4 on the Delta 44. If there's more guitars and/or a keyboard, I'll group a combination of guitar, keyboard, and bass to 3/4 sub-out and run that into input 3 and 4 on the Delta 44.
I will likely get another Delta 44 in the near future when I see another used one up for sale and team them together to give me 8 discrete tracks so that I don't have to use the sub-outs and just run each channel of the mixer to it's own input on one of the Delta 44s.
If your Dad's planning on doing overdubs (and recommended if he's really serious about the end result), he can probably get away with a 4-track interface for now: any more than 4 mics at a time for the drums will require some grouping to sub-outs, however, but with a little trial and error, he can make sure that there's a good overall sound.
As for mics, I've always liked Shure SM-57 microphones as you can use them for close drum miking, guitar amps, and vocals (although I prefer an SM-58 for vocals). These mics have been around for years and can be had for fairly cheap second-hand. There's probably a ton of good mic options nowadays, however.
Definitely get XLR cables for your mics and use TRS balanced cables for your inputs and outputs.
For monitoring, well, I've always just used my Fostex "studio" headphones I've had for years, but I just bought a set of M-Audio AV-40 "Studiophile" speakers. I can't afford the luxury of rearranging my entire office just to accommodate proper near field monitors as I need to do real work in there and fit my multiple LCD monitors as well as the speakers, so these were a good compromise for me. However, the M-Audio BX5a Deluxe are really nice, so if there's going to be a purpose-built recording/mixing desk in the basement, I would spend the extra on monitors.
Hopefully this helps. If you have specific questions (and a rough budget along with expectations for the end product), update your questiona accordingly.