The Line 6 UX series is meant to take your guitar's DIRECT INPUT (DI) and add modeling to it to simulate a mic'd guitar amplifier. Running the preamp out of your amp into a line level input will just be a fizzy mess until you apply IRs simulating the rest of the chain (amp, microphone, room).
Please note: if you are using a valve head and are not connecting a loudspeaker, you must put a load onto the head or it will blow up; valve amps must see a load at all times. Some amps have an internal load, but you have to make sure yours does if you are running the head without a cab attached.
A far better option would be to invest in an inexpensive USB interface and an SM57, mic the guitar cab, and let 'er rip. Behringer and Focusrite both make units that are very affordable.
When you say an 'old' computer, how old are we talking about here?
Recording ANYTHING is basically the same: get it right AT THE SOURCE and you will save yourself much time and trouble later.