Cold start rpms and 1st gear shuttering

I've been having some weird troubles with my 2006 legacy gt. The first few times I push in the clutch to change gears (at about 3000 rpms and only for a few minutes after the first start of the day), the rpms rise a little and I have to wait a few seconds for them to fall back down in order to change into second gear. Also, when the rpms rise I hear a noise that's a mix between a grinding and a fan hitting something. I don't know if it's related but the car also shutters when I try and move from a stop into first gear for the first few times of the day, and then the shuttering goes away. Anyone know what may be wrong? My car only has 81,000 miles. I bought it with 76,000 and it's been happening since about a month after the purchase. Thanks a lot.