You are very likely to end up with a car that spins-out or gets very sideways if you have too much grip differential in your tires front-to-rear. All due respect, there are a lot of limiting factors on a mostly-stock Accord. Body roll, shocks, transmission, etc. Better tires will help, but only marginally. I would try for a matched set of used summer tires from another competitor on a cheap set of extra wheels, then focus on becoming a good enough driver to maximize the car you have. Yes, it will be a little frustrating to be off the pace, but no amount of work or parts will make the accord a front-runner.
Have fun and learn, then consider finding a fast car to codrive in, or shop for an autox ride of your own. Everybody goes through this part of the process (and its always frustrating when you are excited about getting faster), but it WILL make you a better driver if you learn to drive what you have, and avoid trying to mod or spend your way to speed. I see too many drivers who can't be fast without r-comps and highly-prepped cars, since they never learned to drive without the crutches first.
Good luck! If it helps, I started autox-ing in a bone-stock Yaris on oem tires at the same time as another local started in his 4-door AT Accord, and we both eventually became pretty good STR-class drivers, but we both spent 1 or 2 seasons in our grocery getters first.