If you want parallel signal paths "on the cheap", then look at the Line6 POD HD500x. You can pick up a good one second hand for between £200-250, add about £20 for the HD Bass pack (or go the whole hog & get the HD Fully Loaded pack with loads of guitar amps/cabs).
Been using one for a good few years now, really happy with the sounds I get from it, the effects are great too, plug it in to your amp's Effects Return. Add in the all the connectivity you want for the studio (Pro or Home), as well as a sturdy package that is just as happy on a stage. Yes, it's "old tech", but it still works, it still sounds great, and it's still being made & sold by Line6.