Baen's author list isn't a good fit with your current favorites, but I would read the following five first:
- 1632 by Eric Flint
- On Basilisk Station by David Weber
- Oath of Swords by David Weber
- Fallen Angels by Jerry Pournelle, Larry Niven and Michael Flynn
- The Mountains of Mourning by Lois McMaster Bujold
The first three are each the 1st in a series. Fallen Angels is a one-off, but worth reading as are the non-free Oath of Fealty and The Mote in God's Eye. The Mountains of Mourning is the only free Bujold, it is a good, but perhaps not the best, intro to the Vorkosigan Saga.