It's often difficult to answer this, as a home sewer, because you know your own machine, maybe a bit about a fellow sewist's machine, and maybe you've used one on a course.
I would often in the past, recomenmd going to a really big sewing machine shop with plenty of second hand models, asking the staff, and trying them out.
However, I am prepared to say that I used a Janome machine when at Michelle Pye's courses, and was very impressed. Those models would be well within your price range. So (just) is the Atelier 3, which has a number of stitches & features that I think might suit you., but not true overlocking.
Are you able to get somewhere to try them out? I would try contacting the UK HQ to ask to which shows they are taking which models. Or if you are handy for one of the big retailers - but always check what they have in stock.