With one or two exceptions, there isn't really much difference in function or performance between straight-sided and bevel-edged chisels. I think traditionally, joiners tended to use straight-sided firmers, and cabinetmakers leaned towards bevel-edged, but that wasn't a hard and fast rule by any means.
However, not all bevel-edged chisels are equal - some have finer lands than others, and are therefore capable of getting tighter into angled cuts such as those found on dovetails. Some 'bevel-edged' chisels (most modern ones) are little more than straight-sided firmers with the top corners ground off, leaving lands of 2 - 3 mm depth, so are rather less able to clean right into sharp angles. For most woodworking other than fine dovetail work, that doesn't really matter very much. As long as your chisels take and hold a sharp edge, and are comfortable and balanced to use, you'll get most things done just fine.
Since most modern b/e chisels don't have fine lands, some of the niche manufacturers have started to offer specialist 'dovetail chisels' specifically to allow the cleaning up of dovetails right into the angles. Very nice they are too - and with a price tag to match. However, a good quality vintage bevel-edged chisel with nice, fine lands will do that job just as well. You don't need that many, either - a couple of small ones, a couple of medium ones and a couple of biggish will cover all evenualities - say 1/8", 1/4", 3/8", 1/2", 3/4" and 1 1/4". (Chris Schwarz in 'The Anarchist's Tool Chest' reckons you can do just about everything with these sizes, and some people say even this number is more than you really need.)
On morticing, there is a good argument for finding a proper mortice chisel. A bevel-edged chisel would not be ideal here - the thin edges would leave a raggy side to the mortice. It's perfectly true that mortices can be cut with firmer chisels, but sinking a mortice involves some fairly brutal chopping and (perhaps more pertinently) levering out of waste, which a heavy-duty specialist mortice chisel is built to do, but which can be rather too much for standard bench chisels, especially in the harder woods. Since much furniture work tends to use 1" sawn timber planed to about 3/4", and the recommended size of a mortice is about 1/3 stock thickness, you can do an awful lot of furniture work with only one mortice size - 1/4". If you propose to do joinery work such as replacement doors or window frames for the house, you'll need a couple of larger sizes - say 3/8" and 1/2" - but you can always pick those up off Ebay if you need them.
If I were starting again, I'd aim for about 5 or 6 fine-landed b/e chisels ranging from 1/8" to 1 1/4", a few straight-sided firmers for general chopping duties, and a 1/4" mortice chisel. I'd add to that collection a couple of out-cannel gouges and maybe a couple of long paring chisels, but only if and when I felt I needed them for a specific project.
Hope that helps!