A new tire is fine but you need to make sure you are using proper technique when mounting. Once you have mounted the tire and tube completely, push the valve into the rim hole, (this helps make sure the tube is not sitting under the tire bead) and then push the tire down into the rim. Inflate to about 30 lbs, check seating all around and adjust as needed. Then inflate another 20-30, check again and top off.

Also, if you have a blowout don't bother looking for tacks, rough spots, rim strips, etc. Blowouts ONLY occur if the tube escapes the tire, either between rim and bead or through a large slit or sidewall failure in the tire. Blowouts are always either cause by poor mounting technique or tire defect (well, very rarely by overinflation).