For your budget that's really the only (new)machine that would fulfil your needs.
there are a few on here who have that machine, generally they seem well liked.
The ifl 170 is 70 quid more but also worth a look, alternatively you could take a chance from European sellers which would come in cheaper but don't expect Much in the way of back up if things go wrong.
Alternatively you could buy separate mig (gys smart mig get decent reviews, about 380 quid) and small inverter to tackle the stick side of things.
Or you could look for secondhand, sometimes some bargains come up on here in the secondhand section.
Don't forget to add a budget for helmet, gloves etc as well as gas for the mig.