Speaking of cheap, I use what is now a rare guitar but at the time was the dirtiest of the dirty cheap recording guitar called an iAxe 393 from Behringer. This baby was super revolutionary for its time, featuring a USB port next to the aux jack, so I can plug it straight into my computer and record.
These days that's done with special cables or the traditional way with interfaces, but this thing actually works great. Very low latency for a USB powered recording tool. Plays more or less like a standard, cheap-end strat.