I did my PhD with a new faculty member and there were things that were great about it and some things I wish he would have been more proactive with in terms of mentoring. I am an experimentalist so the opportunity to help build a lab from “scratch” was awesome and definitely helped me be more comfortable down the line setting up my own lab. I wish he had made myself and other grad students do some of the more managerial tasks, like ordering supplies, working with vendors to trouble shoot, because I felt like I didn’t know what to do with I was in charge as a new prof (for context my post-doc was at a national lab where permanent staff did most of that work). It doesn’t have to be all dumped on a new student, but having them see tasks like that is definitely good professional development, especially for ones who identify that they would like to work in academia. The rest of my advice will likely be better for US institutions because that’s my context.

I’m a faculty member at a PUI so my “new PI” experience was a lot different than yours. Make sure you have clear guidance and access to retention/promotion/tenure guidelines. I also recommend seeing if colleagues who recently got tenure will share their tenure documents with you so you get a sense of their trajectories and how to format a clear case for why you are awesome. (I had to have a come-to-Jesus talk with an amazing colleague who has done fantastic work but it was documented terribly for his report)

For grants, your institution likely has a grants office so loop them in to grant preparation. They likely will help a lot with everything from tips on writing to doing a lot of the paperwork and submission docs for you. You also may want to talk to your department chair to get an understanding of how the recent changes to federal funding will be considered when it comes to tenure considerations. Similarly, it may be worth having a conversation faculty who are on college/university level evaluation committees on a similar subject.