At a basic level, you need an audio interface, AKA something to get the audio into your computer and, for acoustic guitar (or for recording the sound of an electric guitar amp/cabinet), you'll need a microphone of some kind. The "USB adapters" that you've seen are simple audio interfaces.
Many audio interfaces have USB connections and should work with Audacity. In general you'll plug your mic's XLR cable into the interface, which then plugs into the computer.
Specific product recommendations aren't that helpful since the market changes every year or so, but you can search any online music retailer and sort by price, find something that looks like it'll work for you, and then check out reviews online. There aren't a lot of "absolute crap" devices out there for simple home recording, save for the occasional device whose drivers are so bad they crash. Reviews will generally mention this.
Buying audio hardware is kind of like buying guitars - you probably won't get exactly the right one the first time, but you'll probably get one that's plenty good to use while you get used to what your personal needs and preferences are. If you decide you need something more or different, you can sell it and buy a different one later.