I fly on Q400 Dash-8s a reasonable amount (probably up to 16 trips this year) they're fine (usually) with multiple pieces but if you've got a wheelie right at the limits it will struggle to fit and may have to go under the seat in front of you - Dash 8 overhead bins are too small to accomodate those max quoted figures - there is usually a passenger complaining that it won't go in but meets the spec. If they take it off you at this stage you probably wont be charged and it'll go in the hold but you'll recieve it on the tarmac at the destination though.
Personally, I go for a soft rucksack/knapsack or laptop bag, rather than something rigid unless it is smaller than the usual "biggest ryanair will accomodate style bag"
On regional journeys I've found hold luggage gets out very quick, probably because they don't have to scan it to see if you've been smuggling 2,000,000 cigarettes in to pounce on you going through the nothing to declare lane. Longest I've spent at a baggage carosell this year is 10 minutes. It's usually more like 5. YMMV
Flybe are a Low Cost Carrier, so IF it's full and IF your baggage isn't compliant or IF you have more than 1 bag and it looks like you're really taking the Michael, you might get stung (not seen it, not happened to me, not heard anyone complaining vocally about it in 16 flights - so unlike whizz air/ ryanair from my experience.)
Though that might be because everyone is deaf from the turboprop... If you're going to make a habit of it I reccommend noise cancelling earphones.