When going to alto sax from the clarinet there are some important points to remember:
Angle of mouthpiece
Clarinet - goes down 45 degrees
Saxophone - goes straight into the mouth
Embouchure
Clarinet - "EE-OO" tug-o-war with the muscles ends in a tie resulting in a flat chin
Saxophone - same "EE - OO" tug-o-war, but the "OO's" win, chin is rounded but not bunched
Air
Clarinet - generally faster, colder air blown against lots of resistance
Saxophone - generally slower, warmer air with little resistance.
Mouthpiece pitch
Clarinet - plays at or near the top of its pitch, you can't "lip up"
Saxophone - plays closer to the center of the pitch, mouthpiece and neck should sound Ab concert on alto
One of the most common problems I have found when teaching sax students to double on clarinet is that they miss the clarinet's resistance when blowing so they unconsciously constrict the throat to have something to "push against". The other is that they play with too tight an embouchure and get a pinched sound that is sharp---especially in the high register. If you keep these things in your mind when practicing, you will do fine. The Fobes Debut would be a good inexpensive mouthpiece to start out on. In the limited time you have, a mouthpiece with a wide open tip may not be the best to start out on.