Ouch! Grinding gears!

I have a 96 civic EX 5-speed and every once and a while(it's becomeing more frequent) it grinds in 3rd, even with the clutch in all the way. I've noticed the clutch is beginning to slip, so I'm needing to get a new one. I was wondering, will the new clutch fix the grinding issue, or will I have to get the tranny looked at too? Thanks!

It's a commom problem for 3rd gear syncros to go out. It would be cheaper to buy a used transmission that wasn't grining than to pay to have it fixed.

About how much do you think I'm looking at to get the syncro fixed?