There are a few options. I would not recommend the USB mic, as they offer limited monitoring capability and if you decide you want to record with 2 mics at one time, you'll be putting the USB mic in a box, because it won't allow you to do that.
1) Portable stand-alone recorder - the
Zoom 4HN is at the top of your budget will do exactly what you want (assuming you are not 1-man-banding it!) and should not be too challenging technically, it has built-in mics, but also allows plugging in external mics or instruments.
2) Microphone(s) and audio interface and recording software - this is going to probably exceed your budget, but will allow expansion/upgrading of equipment as you get more experiences or want more options.
Reaper is free to download, $60 to register. Adobe Audacity is free and may suit your need but its editing features are somewhat limited in comparison with other full-featured DAWs
Audio interface - probably the least -expensive you would want to look at would be the
Behringer U-phoria 204 - at $80, its a decent starting point. More money will get you better quality and preamps.
Microphone - many many choices, but a single LDC (large diaphragm condenser) mic would do to start things, the
Audio Technica AT2020 for $100 is highly recommended.
Either choice 1 or 2 is going to have a learning curve, and 2) will require more, so a lot depends on how technical you are and how much learning you want to put into recording.
You are also going to need a way to monitor your recordings - multitracking means using headphones (closed back are best), and monitor speakers to hear your music when playing back. Using the Zoom recorder, you will still be transferring your tracks to a computer to burn a CD or to post online and eventually you might want to use it just for recording tracks, then doing your mixing on the computer.