Nostatic posted the best reply question: What is your goal?
Not to bore you with my background but part of it is that I did spend 3.5 years as the sales manager for a digital audio sound card and studio gear manufacturer, and Im pretty familiar with the industry on both the hardware and software side. I used to use Pro Tools exclusively on the Mac but now that I am on PC, I used Sonar and I love it quite a bit. It is a stable product, that sounds great, is easy to navigate through and use, and the MIDI capabilities are perhaps the best in the industry as it started out years ago as Cakewalk and MiDI product only at that point.
Currently Im using that product and also my former companies soundcards and digital clocking unit (note that my former company is now defunct as of a couple years ago, but the units were among the top of the line in their heyday 3-5 years ago).
to your questions:
What is the modern equivalent? Will a standard PC sound card be sufficient to digitize the signal, either real-time or from another recording device?
* I would say No to that, unless you want to just hack out some simple demo-quality songs...but to do pro-quality, you will probably need a pro audio sound card that has a) professional inputs and outputs b) quality a/d and d/a converters and clocking c) low latency recording capability (aka no delay between what you play and how long it takes the computer to record and play it back) d) good to great driver and software compatibilty support e) great sound. f) how many inputs do you need? are you tracking an entire band, or a drum kit, or do you work alone solo? g) what type of inputs...are you doing any micing or is it all 1/4" inputs, do you need MIDI i/o? digital i/o?
Does anybody still record on DAT?
Not really except for some master down to DAT, or use it for achieving. It is still a viable format but less and less in the recording "industry" as hard disk is much cheaper, faster and easier to backup.
What is a good cheapo mic for recording vocals and acoustic guitar, an SM58 or something? Isn't an SM58 balanced output? How would you get that into a computer?
SM58 or 57 are good to mic guitar amps but as a dynamic mic, wont be your best bet (usually) for micing acousic guitar, or vocals (though it highly depends on what you are trying to mic and what "sound" you are trying to get... a 58 can sound good on vocals (Lennon used one extensively in the studio) but it will sound entirely different than a higher quality condensor...also it depends on what type of music you are recording...rock, jazz...blues...classical...voice etc.
Is there a piece of software recommended for multitrack editing?
Pro Tools is kind of the industry standard, but is expensive for the typical beginning home recordist with the interfaces that you would need. A better option would be to look into Cakewalk Sonar, Logic Audio or even Steinberg Cubase or Samplitude, other options include Adobe Audition and other software including loop-based that are more for techno or dance music.
I think a great thing for you to do is to check out some recording forums such as
www.audioforums.com www.homerecording.com and others to check out what they have. Sonar has a great user forum too if you want to learn about their software at
https://forums.pelicanparts.com/forum.cakewalk.com
the considerations that you should look at are your budget, your expectations, what music you are going to record, what are popular soundcards...be very careful with reviews, and only use them as backups to make your decision. Reviews are quite often skewed heavily by advertising dollars... good luck let me know if you have specific questions about anything and we will try to help