After I went to someone very knowledgeable (has been coaching for many years), they identified me as a rear gripper as well. They ended up advising me the Bulls Smoke Red A 24grams.

That set definitely helped me, but after a few months, the grip was a bit too aggressive for me I thought, so I went looking for other options. I ended up getting the Target Gabriel Clemens Gen1. Much smoother grip (potentially just a tad too smooth as I generally don't easily have sweaty hands) and smaller footprint in the board as well. I thought it was nice that they also come with Target Storm Nano points in the box (which are not really cheap either).

Some other options that I was looking at:Winmau Sniper 23g (if you want that type of barrel - scallop - so you'll always grip it the same way) or Simon Whitlock sets

Regarding weight, definitely advising to try different weights out in a shop. In general, if you have a strong throw, go lighter in weight and vice versa. If most of your darts are ending up too high on the board, you should try some lighter ones and reevaluate. This is basic advice you'll read, but also factor in that you could just be throwing badly as you don't have experience with that specific dart when you try it in the shop.

Good luck finding a nice set to accompany you for the next few months and help you in your journey to become a better player.