CIT has been fine for me, I have no issues with transfers in or out, always done quickly. I have used them for wire transfers multiple times and it's free which saved me a fair amount money in wire fees, their rate is above others.
I would find a bank that offers a deposit bonus up front though. I just got a $1500 bonus from Capital One. Discover usually has bonuses, smaller ones, but they also tend to offer bonuses after account opening as well. For example right now I have an offer to deposit 40k for a $250 bonus into my existing Discover account. So I will move money over there and then likely move it back to one of my HYSA with higher rates once the bonus hold time has been met.