Mix up the fast, faster, slower and slowest tunes. Playing two slow pieces back to back isn't bad, but make sure there's a peppier piece on either side of them. Same things with tunes that may have "down" connotations or words; they should be followed by something more upbeat. For example Streets of Laredo and St. James Infirmary should not follow each other. Both are beautiful tunes but the subject matter in both is depressing (death & dying).
Make sure you really DO play tunes at different speeds; many groups have a tendency for all the songs to slump down to a common, below normal, speed.
Start and finish with songs your audience will know by heart -- tunes from the 1940s - 1960s. You Are My Sunshine is always good. Also Tennessee Waltz and Danny Boy. A mixture of folk and popular tunes with a hymn or two like Amazing Grace and Simple Gifts thrown in goes over well. Mix up the "ethnicity" of the songs too -- American, English, Celtic, etc. Do, please be aware of copyright and performance rights issues. Public domain songs are the best, always. You can play Aura Lea, which the audience may recognize as Love Me Tender, but tell them Elvis "borrowed" a much older, public domain tune, and wrote his own words for it. There are several other examples
Playing songs alphabetically is. frankly, a bit weird. Number the songs as they will fit in the set/play list. Make them a printed "playbook" with each song, in order, stapled together at the corner.
I would start with your BEST tune, not necessarily a fast or peppy one. Don't assume the audience will know all the tunes -- announce the name of each one, with a bit of background if you can.
Just a few thoughts while floating on the river aboard the s/v ManCave thinking about what I'm going to perform at Monday's Open Mic...