"Cheap" models are likely to have a slow action and require more push n pull to get notes to sound.
Sometimes you might have tuning issues on individual notes, or some notes will only play with more air (relative to the others on the instrument).
You might find stuff like leaky bellows or sticking keys if you buy second hand (eg eBay).
I got a Rochelle C/G which was new, no major issues, most notes sounding with moderate air, and tuning was good (checked on an electronic tuner).
Within 2 weeks I have 2 tunes playing ok and at a "normal" session speed (Mist Covered Mountains, The History Man) and a few in the works. I am now thinking the slow action of the instrument is holding me back a bit but thats ok until I have a few dozen jigs n reels and I want to play out in the pub. The Anglo is good for playing chords and I have used it for that during some stuff I play with my musical mates, giving a nice backing with the other guys when someone is singing. Easy to do with a little musical knowledge.
I have tried a mate's Morse English and found it has a much quicker action and draws/pushes notes with a lot less movement of the bellows.....so I guess I realise that I will need a better instrument in order to play at session speed without all the current effort that I have to put in.
But which make? What price?
Is a Marcus the one? Or an mid-priced Lachenal? Do I watch the internet bidding sites and then gamble on something I've never seen or played? Do I make a road trip to a far away concertina dealer and trust their judgement and help with one, or do I just email them or ring them up and tell them my budget and hope they don't take advantage?
Finding the next instrument is going to be a challenge. Not much out there that I have found that helps you really choose. Ideally its best to try a few and buy what you feel best with, or so it goes with pipes and flutes. I think 'tinas are just the same.
The Rochelle is good. You could get cheaper second hand stuff (with issues) which would still allow the learning of slow tunes.
I already play a handful of other instruments so I had a head start. If you are new to music, a beginner instrument would see you through at least a year of learning.
A really bad beginner instrument might just put you off for ever !!!