Here is a simple idea that I applied yesterday to my team that, among other things, helped me win the challenge.
Look for inexpensive players either who are new to their MLB teams, added at the last moment or who are replacing an injured full-timer. By having one or two of them will leave you sufficient money for elite players elsewhere.
Incidentally, with today's limited schedule, I would not go cheap on pitchers and outfielders.
Here are potential inexpensive fill-ins active today:
C: Stephen Vogt ($2,200): Had a HR last night.
1B: Steve Pearce ($2,700): Not that inexpensive, but still at a reasonable price.
2B:Jace Peterson ($2,000): He helped me yesterday.
SS: Nick Ahmed ($1,600): Should be full-timer with Diamondbacks.
I will be out of the country the next three weeks, so you will not be playing against me, but good luck playing against my fellow Mastersballers in the interim.
Pasko Varnica writes about present day fantasy sports and about sports in Rome in the ancient times. You can find his work at Sports in Antiquity.