I am installing a small SOHO router/switch and connecting it to two other switches elsewhere. Do I need to worry about setting up Spanning Tree Protocol for best results?
No, you dont need, nor want STP.
STP simply ensures that there are no network loops (switch a->switch b->switch c->switch a). It can be used to provide a redundant connection between switches, or provide least cost routing in a larger network.
For a home setup -- absolutely not. It will be more headache than you will ever benefit from it. Even with more than a handful of switches a careful evaluation and configuration needs to be ensured. Typically vendor A's STP implementation can cause issues with vendor B's STP implementation. HP even had me disable STP between revisions of their Procurve switches.
More details are on the Wikipedia article.