You don't get typed at the drive during the pre-screening, that happens at the lab after donation. If you have donated before, your type will beon record but each unit is typed independently of who donated.
All of the common blood types (O,A,B,AB) also have an Rh facor (positive or negative). The only "rare" type is the one that isn't on my shelf in the blood bank when I need to do a crossmatch. Yes, summertime is definitely a time of shortage- please donate. O pos (the most common type) can be "rare" when folks aren't donating as much as they used to. Some of the largest sources of donated blood are schools (closed during the summer) and corporations (closing due to economy). Approximately 5% of the population donates for the other 95%. I always tell people who can't donate (for many, many reasons) "Yes, but you can help encourage those who do or those who never have".