It would be useful if you could quantify "modest" and then we can recommend the best gear for your budget
If you already have a powerful enough PC then you can get "free" multi track recorders such as Audacity and/or Reaper, as well as the Computer Music Magazine one found on theor cover CD
The main thing to look for on an audio interface is the number of inputs/outputs and the quality of the pre-amps
The number of inputs can be confusing as you will need to know how many you want to use SIMULTANEOUSLY
If you are recording to a backing track you could import/record this first and then overdub the vocal
If you are recording stereo you need 2 tracks to record simultaneously (left & right)
Once this is done you can "overdub" guitar & vocals
You can either do this "one at a time" using the multi-track or many people like to do it at the same time to get a better "feel"
If you do this you will need at least 2 inputs simultaneously
You can do all your mixing within the DAW
I would recommend MAUDIO or FOCUSRITE as brands with good "bang for buck"
This is a popular AI, is good value and gives you some room for growth
http://www.dv247.com/computer-hardware/focusrite-saffire-6-usb--67804Here is the baby brother:
http://www.dv247.com/computer-hardware/focusrite-scarlett-2i2-usb-audio-interface--90034There are also some good bundle deals available with mics
Good luck