Software wise I would recommend virtual instruments in your DAW. Unless you are using something extremely limited like Audacity, your DAW should support virtual instrument plugins. There’s a lot of drum kit VSTi’s out there. GarageBand/Logic is the easiest here, tons of “drummer” audio plugin units just to download. But the other major DAWs all have good support here too. I use it VSTi’s heavily in Reaper, for example.
Another option is to get a dedicated drum machine. I like having one because (a) I am old school that way and (b) I think they are nice, tactile, fun instruments on their own. But for someone starting out now I would instead recommend just using virtual drum kits in your DAW - it’s easier and more flexible.
As for where to start pattern-wise, four-on-the-floor! I’m not even joking, it should absolutely be the first pattern you learn to program because it will teach you how to use the drum/MIDI sequencer in your DAW. (VST’s use MIDI to program the virtual instruments.)
As for learning drum theory, if you find a good site online for this that is focused on MIDI drum programming I would love to see it too. I just figured it out on my own back in college (it was one of the things I did for our band) and that is definitely not the best approach
Using the MIDI step sequencer to program drums is not rocket science, though. You should be able to come up with interesting kick/snare patterns on your own. What gets much more interesting is good use of things like syncopation, fills, and the cymbals. And a course on programming those would be a good find.