Tires & Wheels

I recently went to get new tires on my 98 Neon Sport. I wanted a little bigger foot print and lower profile, so I went with a 205/50R14 mean lookin directionals from Kelley. The fronts fit just fine, but the rears rubbed up against the trailing arm. So I ended up stuck with some no frills all season 185/65R14. They do not handle as well as the OEM Goodyears that were on originally. I also recently bent a rim and will be needing to replace it, so I was thinking of atleast going to a 15". What I am concerned with is the trailing arm. Has anyone run into this problem and if so what is the fix? What are my options for tires and wheels?