The Side Imaging units allow you to look 100'+ to either side of the transducer as well as directly under the boat. You can see structure & fish which aren't directly under the boat. In theory, considering your normal haunts, SI would be the best for you. You can see a lot of water even when shallow. You can see under docks and around bridge pilings. You could see a little of what was against the banks. In practice, except in ideal conditions, you don't get much target separation in very shallow water and it would be very difficult to pick out fish against a bank or under a dock in 3' of water. Biggest issue is you won't get one for under $500 that I know of(more like $800 or $900 for a good unit). While it might be the best, it's probably way overkill for what you do.
*Side Imaging is the same technology as Down Imaging it just "looks" out in 2 directions instead of just straight down.
Down imaging, just like traditional sonar only "looks" directly under the boat so you'll be getting a very narrow picture of that unless you're in deeper water. The thing I like about DI is that it draws a pretty good picture of what is directly under the boat. I cut my teeth on the old flasher units and have slowly, sort of, kept up with the technology. I could pick out fish on the flashers, the graph type units made it easier, but the DI makes it a no brainer. What I like best though is the ability to make a good judgement on the type structure I'm passing over. Trees are obvious, there's no guessing. Rocks and oyster beds show up pretty clearly, and it's fairly straight forward to pick out individual fish, even small ones. (They don't look like fish of course, just blobs.)
In shallow areas no unit is going to give you much of a picture and a lot of times all you can hope for is a good depth reading. For your kind of fishing I think you've got your budget set about right ..... prolly $250 is all you need to spend unless you want to add GPS. The HB 346 will give you a good(not GREAT but good) DI unit, a traditional 2d color picture and accurate depth readings in shallow water. It's compact but the screen is large enough to see pretty well. I like the HB 561 but IMO trading the slightly larger screen for color on a little smaller screen is worth it. Color readings are much easier to interpret.
The one thing I will say is if you're willing to bump up to $300 - $350 you can add GPS to the mix and it's a good addition. You can mark specific spots, get a general map of the body of water you're on and gauge your speed very accurately(important for trolling). I feel much more confident leaving the ramp before daylight and have at least one time used it to find my way through the fog. I like being able to mark the ramp and wander new waters all day knowing it will be easy to retrace my steps when it's time to go home.