Approximately...
REAPER - $60
An audio interface - $100 and up
A microphone - $100 and up
Hopefully, you already have some headphones and some computer speakers that you can use for monitors.
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If you are full-MIDI with no audio recording (and of course no vocals) that can be done entirely in software.
If you're not multitracking you might be able to get-away with Audacity (free, open source) instead of REAPER. Audacity can't really multi-track record, but you probably aren't going to have a multi-channel interface anyway. It can
mix multiple tracks but it's not really the best tool for that.
A keyboard line-output or headphone-output can go-into line-in on a regular soundcard on a desktop/tower computer. The line-input on a soundcard is often quite good so you can get-by without an interface.
Most laptops don't have line-in and the mic-in on a laptop or soundcard is virtually useless because it's "wrong" for any good stage/studio microphone. You'll need an interface if you expect to record with a good microphone. You also need an interface to (properly) directly record guitar/bass. Many interfaces have switchable mic/instrument inputs.
The microphones built-into a smart phone can be pretty good, but they are not directional which means they pick-up noise from all-around whereas the signal comes from one direction. It could also be tricky synchronizing a backing track.
Laptop mics usually aren't that good. They usually pick-up fan noise, hard drive noise (and keyboard noise, etc.), and they are hard to "position".
The most common
type of mic for studio recording is a "Large Diaphragm, Cardioid (directional) Condenser". They are used for vocals and almost everything else. But, they do have electronics inside and they can sometimes be overdriven (distorted) if you put it in front of a kick drum or loud guitar amp.
There are some "cheap" ($20- -$30 or so) electret ondenser microphones that "look like" studio condensers sold by 3rd-party Amazon sellers, etc. Obviously, there is more money put-into the case, cable, and accessories than the functioning part of the mic. These mics may be "useful" but you're not getting the "real thing".
The most popular microphone of all time is the Shure SM57/58. It's a dynamic mic (not a condenser) and it's really meant for live use, but "you could do worse". (The 57 & 58 are virtually the same, but the 58 has the ball pop filter for vocals).
You may eventually want a pair of "matched' mics for stereo recording.
You can get darn-near professional recording for a few hundred (or several hundred) dollars (depending on the number of microphones/channels). The thing that can get REALLY EXPENSIVE is soundproofing and room treatment. You'd also need to spend a few hundred dollars on decent monitors.
...This stuff is relative cheap! Before "digital home recording" and affordable audio interfaces (and MIDI) it would have cost thousands of dollars to set-up a home studio with nearly-professional recording capability.
Quote:
I can only spend about 100 bucks on my recording "hobby" as she calls it.
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Well... Apparently, it's not a business.
I'm pretty sure most REAPER users are hobbyists.