IMac – Booting iMac (2011) off of external SSD

First, I'd suggest making a plan for deciding what data is going where. A simple starting point is put all your media (particularly videos) on the hard drive, since it often accounts for the bulk of the data and benefits less from the speed of the SSD.

Secondly, you can customize what data Migration assistant brings over. Have it transfer your apps and settings, and maybe the basics from your home directory, then once you've got your system up and running you can transfer the rest either by running Migration Assistant again, or manually via Target Disk mode.

Another option, if you have a bunch of data (enough to get you under the 256GB barrier) that you know you're going to be putting on the HD, is to transfer it manually first (or to a backup drive), then delete it and run Migration Assistant without any exclusions.

Was the mac shipped with 3gb ram? It is possibly not the reason but advice all the same, apple strongly recommends you run ram in identical pairs or individual modules, so a single 1, 2, 4 etc GB stick or 2 x 1, 2 x 2GB and so on, but not 1 x 1gb and 1 x 2gb.