The all-in-one solution is an amp modeller with USB audio connectivity. You plug the guitar (input) and headphones/speakers (output) into the amp modeller. Audio is transferred to the computer over USB.
If you are struggling with your recorded guitar tone then I suggest this approach.
Examples (ordered by price, descending):
These are medium- to entry-level products. I haven't tested these pedals but they have the feature set that is required for an all-in-one solution.
You also need to make sure your guitar is producing a clean signal. That means making sure there is no hum/buzz from single-coil pickups or the guitar cable. If you are not sure, try taking the guitar and your guitar cable to a music store to plug into an amp; if it sounds good and there is no noise then your guitar/cable is fine but you may be playing in a room with electrical interference at home.
At that point you achieve low-noise audio recording. There is higher-end gear that can produce more detailed amp simulation and effects, but all three multi-effects units I mentioned cover the basics.
Personally, I currently use a modular solution instead of all-in-one: Focusrite Scarlett 2i4 USB audio interface, S-Gear amp simulation software, MainStage MIDI automation software, and Behringer FCB1010 MIDI foot controller. The price is similar to the Line 6 POD HD500X, maybe a little more expensive, but it gives me more options and I prefer the amp models. The problem with the modular approach is that more things can go wrong so I don't recommend it unless you are already comfortable and want to explore more possibilities.