There's no law about only using a tenor for blues.  It's just a lot more common than alto.  It all hinges on your own preference for your own sound.  There have been a lot of fine blues sounds on alto.  Eddie "Cleanhead" Vinson, Earl Bostic, Cannonball Adderly, Jackie McLean, Lou Donaldson (with Art Blakey), Gary Bartz .... even Charlie Parker had the blues at the core of his sound. 


The Alto is in the key of Eb, which is a fourth above Bb, the key of the tenor.  Guitar-based blues are most commonly in E, A, and D.  On tenor, that's F#, B, and E.  On alto, that's B, E. and A.  So you're going to need facility in keys near the bottom of the circle of fourths regardless.  Should you ever decide to take up a Bari sax, that's in Eb like an alto.


I'm partial to old Martins and Conns for blues.  I played blues for years on an old Martin Indiana tenor.  They're not tremendously agile in their handling, but they can have a gutsy sound.  There's a guy in town who sounds good playing blues on a Martin Imperial, which was Martin's second line horn after the Indiana.   Martin "searchlight" and "The Martin" horns are great too, but they're going to cost more.  It's hard to go too far wrong with old Conns for blues.  There are some differences between the sounds of the "Chu Berry," early and late "lady on bell," and "shooting star" horns, but they're all big and fat sounding.  The earlier horns can get a sweeter, richer sound than the later ones, which may or may not be important enough to you to justify their higher cost.  You might also consider are the Pan American horns, which were made as a low priced line of Conns before they made the "shooting star" horns.  If you do get a Conn, you want one with"Elkhart, Indiana" on the bell.  The ones made in Arizona and Mexico have a reputation for problems.