EMCD -- IF you're staying with 15" rims (7 and
, truly your choices are very limited.... I can attest to that. As long as the backspacing is correct with your rims (7" needs 4" bs, 8" needs 4.5" bs), the tire will stay in the factory stock location within each wheel well, and you shouldn't have any fender problems or otherwise. For what its worth, as I've just INCREASED the front tire size on my Challenger, from 245-60-15 to 255-60-15, I'd say the ride is better... a slightly taller sidewall giving slight;y better ride siftness, as well as slightly gained round clearance for my headers, etc.... and, I can adjust the ride quality simply by adjusting the PSI o the tires... I've settled at 28 front/26 rear, or bump them up to ~38 f, 36 r for dry road course action (could even be a little higher, say ~40f-38r). IF you do any pylon low-medium speed autocrossing, forget about any quality 15" street tires to do the job... you'd have to get another set of rims/tires for that action if you'd want to be half-way competitive as well as having some increased "fun".
I know that the Mickey Thompsons were mentioned, as well as some Nitto's... they offer some 17" tires with a decent tread wear rating of 300.. and the prices of 17" rims can be found fairly affordable (Year One's rims 17x9 Mopar ralley rims with 275-40-17 tires are an excellent choice. For summer performance, consider the lowest numerical tread wear ratings for best grip. Truly, in my opinion, "grip" won't be noticed on plain street driving... but instead, better noticed on highway type of driving (or road course events for certain!).
Ultimately, you may really want to consider having two sets of rims/tires per your activities. The lower tread wear tires (200-300) (street/hwy allowable) will wear out more quickly with the better gripping; the higher tread wear tires (above 300 say... ~340 and up, but don't go beyond 400 if possible), will last longer IF you want mileage out for your tires and willing to sacrifice grip.
As an extreme example of tread wear grip/life, the Hoosier A6 DOT Autocross tires will last about 60 minutes of autocrossing before throw-away time (maybe less or more pending the driver's style, etc).. BUT... there is NOTHING in a DOT category that grips better (in the dry... and, they also make rain versions of the A6!).... Check out the Tire Rack web site for details of different tires, as a starting point.
Overall, again.. with your 15" rims, selection and performance is limited to us.... just have some fun with whatever you'll get!