You could search for a tank called a "bookshelf tank", these are more popular for freshwater, and sized roughly to fit a bookshelf (very narrow front to back, but very wide left to right).
That type of tank may work, but typically you'd need some space behind the tank for either a Hang On Back (HOB) filter, or an overflow. Certainly, there's other options, but those other options may not be the easiest if you're newer to reef tanks.
Most in reef tank keeping tend to value the front to back dimension more than even height. The reason is that this gives some real depth to your aquascape. And as you pointed out, getting flow right in a very narrow and wide tank may be challenging.
I'd suggest you look for a small All-In-One (AIO) aquarium, such as those from Innovative Marine, for example. You can find AIO tanks from about 3 gallons up to 40 gallons and even larger. But the smaller ones like 10-25 gallons can often fit on a countertop, desktop or even something like a sturdy end table or night stand.
This 15 gallon AIO would be a fine first tank, if you're short on space. Much smaller and you're really limited, much larger and you may need a dedicate stand and floor space. This particular listing appears to be the old price too, so bonus :)
https://www.saltwateraquarium.com/15-gallon-fusion-aio-all-in-one-cube-aquarium-innovative-marine/
Good luck!