I (am fortunate) to have a home recording studio, and did much research on the various aspects of it, including the room construction as well as the equipment involved. It also helped of course that I was familiar with the electronics end of it and mixing boards, from having been a working musician for many years.
For most things, other than acoustic instruments, you can go ''directly into the board'' (mixer) of your multi-track recording unit. (In my case I used a Yamaha MD-8 Mini Disc 8 track, multi-track system, which yields great results - CD quality sounding product.)
If you can afford it, go at least 8 track. You will outgrow a 4 track system surprisingly fast, and develop a lot of sound degenation and ''bleedling'' (one track running into another an losing the clarity of the sound of each individual track) through bouncing (a.k.a. ping ponging ---taking the accumulated recorded tracks and re-recording them all onto 1 single track, to make more room for additional overdubbing on the other tracks.) You can get a great unit such as the Roland VX-880, or the Yamaha MD-8 for 1500.00 U.S. or less.
The Roland has a few advantages in that it is entirely digital (recorder as well as mixer as opposed to the MD-8 having a digital recorder but analog mixer, and no digital out --but there are ways around that--) and the Roland has digital outs for mastering directly to your hardrive or CD copier. It also has built in effects...so you wouldn't have to purchase additional effects processors --but it requires that you have a SCSI based hardrive (which I don't - have IDE) or that you use ZIP disks on some of their cheaper 8 track models. (Personally I've never had any luck with ZIP disks or Iomega products so I avoid them like the plague.) As I already had the effects processors (as the MD-8 was a move up for me) I didn't need the extra bells and whistles the Roland had, and I personally liked the fact that it used Mini Disks. The Yamaha is also more user-friendly and has a better display panel (mutil-coloured fluorescent as opposed to the black text on grey LCD panel of the Roland.)
For recording acoustic instruments (which for me is primarily guitar and voices) I use a good quality condensor microphone, and you should have a mic chord with a powered transformer-ed end (1/4 '' phono jack end) or XLR end (also known as a ''cannon'' end.) My condensor microphone of choice is an AKG C1000S.....which is very crisp and clean. You can also get by with a Shure SM-58 or 57....Good results with either Shure but more clarity and crispiness with the condensor.)
As for the room itself, it is dry-walled and underneath the dry wall, is sound proofing insulation (readily available at most ''do-it-yourself'' builing places, but in addition to the sound proofing insulation (both in the walls and ceiling) there is another WONDERFUL and cheap source of acoustic dampening, that you can use - either in addition to the sound proofing insulation - or as a stand alone - better though if you add a layer of this OVER your insultation, and under the drywall with a seal of vapour lock over everything, beneath the drywall -- that being EGG CRATES!!! Yes eggcrates (the kind you see that hold a dozen or 2 or 3 dozen eggs, that arrive at farmer's markets, etc....work marvelously. I have even been in professional studios that have used them on the outer walls within the studio, and they've been painted in patterns and wild colours, etc. They work just great, and are cheap...
If you plan to do in any recordings utilizing a drum machine, or other multi-source signals, consider investing in a sub-mixer - to have more control over the stereo spectrum of how you want to place (or pan) your instrument sounds, either during recording or final mix-down.
As well, consider investing in a decent compressor (to limit peak signals, which can occur during a vocal or acoustic performance) and as well a decent digital and programable reverb.
Consider, as well the learning curve involved in using all the above stuff together....could take you a month before you have a comfortable handle on the whole process from beginning to end, but an ENJOYABLE and interesting voyage of discovery.
Obviously these are all suggestions AND if you are fairly well heeled and are striving for as professional a finished sound/product as possible out of your home studio.
There are cheaper ways to go........but I can only speak from my own experiences, and the standards that I use for my own projects.