Grass types to plant for front and back yards with different light levels (Zone 8B)

Long story short, I purchased a home that required needing to hire a skid steer to clear the front and back yards due to the previous owner growing a literal jungle. I'm down to bare soil in the back yard, and I grew some annual rye in the front just to stop erosion during the winter. Going to replant grass this spring after spraying glyphosate on everything but want some opinions on what types would work best.

I'm in Zone 8B (SC), and the front yard is ~10,000 sqft. and full sun with a straight tree line against the west side of the property which casts some shade when near it. I was thinking Bermuda for this area since it spreads well and does well in the sun. The back yard is ~ 12,000 sqft. and has partial sun, maybe 4-6 hours due to heavier tree coverage. Due to the size of the area, seeding is all I can afford to do which eliminates St. Augustine.

If I do Bermuda in the front, what could I put in the back? A shade mix with Bermuda? A totally different type? I would imagine if I did that there would be an obvious transition line between species since there's no fence to help separate the front and back yards which is why I'm hesitant to entertain the idea. If a shade mix is the way to go, do you have any recommendations?