OK, that's a start. What microphones do you have? Specific models will let us know where your starting point is. Also, a bit of info on your current computer will be helpful? Processor and memory will make a difference in performance. A solid state drive is great to have, but not an absolute necessity if the rest of the system is powerful enough.
For a basic system, you can pick up a Behringer UMC204HD for around $80. It's a basic audio interface, has two mic preamps which will let you set up a mic for vocals and a mic for a guitar. Or you can record a piano in stereo, then add vocals later. It gives you options. It also has midi, so you can use your keyboards to control virtual instruments later on. If you want a better quality unit, you can look at the Motu M2 or M4, or the Zoom UAC2.
You need a Digital Audio Workstation (DAW). Stay away from Audacity. It's a great editor, and free, but doing multitracking is not it's forte. I would recommend looking at Reaper
and Cakewalk by Bandlab
. Cakewalk is free, Reaper is free to try and $60 for a license. Reaper is a full fledged DAW and can be as basic or as complex as you want. I've been using it for over 5 years. Both come with internal effects called Plug-Ins.
Microphones can be a bit of a rabbit hole. I would avoid the really cheap USB mics and similar Chinese condensers (like the Fifine and ZINGYOU). They work, but really aren't quality units. I've heard quite a few people who end up with non working units. Their only positive is that they are cheap, usually $25-30.
I use different ones for my acoustic guitar vs my vocals. Most of my vocals have been done with a Rode NT1, although I've also used a cheap MXL V67g ($80) and an old Studio Projects B3. I also have a Miktek MK300 that I picked up on sale. It sounds really good, but I haven't used it for real recordings yet. For my acoustic (a Taylor 310 dreadnought) I have Rode M5s and AKG P170s. Neither is a high dollar mic ($100 or less). Those are all condensers. For dynamic mics, I have Sennheiser e935 and e835. I prefer them to the Shure SM57 or 58 but that's just a preference. I also have the 57. Mics will often go on sale so that one that is normally $300 might be $200, or a $120 mic might be $90. Patience is a virtue when you are shopping for mics. Since you already have some, start with those and then spend time learning about mics. You don't need a $3000 Neumann to do some decent recording.
Assuming your computer is good enough and you have a decent mic already, you could be recording this weekend for under $100.