No one can offer a suitable suggestion unless you tell us your general location.

As to the sowing of seed into a different variety of grass....that's never a good idea. We need to know where you reside, what your permanent grass is.

It sounds like you might live in a climate where "warm season " grasses are the norm....in which case, seed won't be much help.

I have never had a grass take over another grass it just gets patchy unless of course you want to plant st augastine which really sucks due to being a weed itself and weeds love it.

u just need to go to the local walmart - they will be selling the correct type of seed for your area, and the bag will have instructions on it - that's what i would do