Yes, a model, type of boat, and type of boating intended would help.
Most people don't split the screen on the small displays, they just switch from one to the other. For smaller boats on inland waters they can work quite nicely without spending a ton of money.
Garmin is known for the best GPS mapping, not so much for sounding.
It sounds like you're on a budget, so yes, a transom mount 'ducer is the way to go. But instead of screwing the bracket onto your transom, mount a piece of starboard there first. You can just glue it on there with 5200, or put a couple of counter-sunk bedded screws in it. Get a scrap piece, like 3-4" by 12". That way you can mount as many doo-dads on the back of your transom as you have need for and not be drilling holes in your boat. You may want to mount a second 'ducer, or a bait well pump, or whatever. Mount it just up from flush with the bottom of the hull.
It's also easy to include a temp sensor in a transom 'ducer, if that's important to you.