For all new (US) faculty, here're the grants I'd suggest focusing on immediately:
1. Innovator - https://commonfund.nih.gov/newinnovator
2. MIRA - https://grants.nih.gov/grants/guide/pa-files/PAR-17-190.html …
3. PEW - http://www.pewtrusts.org/en/projects/pew-biomedical-scholars …
4. Searle - http://www.searlescholars.net/go.php?id=1
5. BWF - https://www.bwfund.org/grant-programs/infectious-diseases …
Go get 'em! 
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Aren't Many of these one or two only per institution so not free for all to apply...?
Correct. PEW and Searle requires institutional nomination and only one per institution. The others (AFAIK) are open.