Suggestions:
1. Exploit home park to the hilt
In Strat, 50% of the rolls are off of the batter's card and 50% are off of the pitcher's card. There are 108 results on the batter's card and 0-8 are homerun ballpark chances and 0-5 are ballpark singles chances. So a power hitter might have 8 BP chances, meaning that 8 out of 108 times a 20 sided die roll will be made and the result based on the ballpark (so a ballpark that is great for homeruns like Polo Grounds will give a homerun every time these ballpark chances come up whereas a pitcher's park might give up very few or none.) Ballparks are rated 0-20 for ballpark singles for righties and lefties and 0-20 for ballpark homeruns for righties and lefties. So a park like the Polo Grounds'41 with 0 0 for singles and 20 20 gives up no ballpark singles and a homerun every time a ballpark homerun chance comes up. So, one way you could exploit that is by loading up on power hitters and then getting pitchers who give up none or few bp homeruns. If you have a ballpark that does not give homeruns you might go with batting average guys, speed guys or both.
3. Get the best pitching you can get and platoon
I don't really play ATG but I remember the simple advice from one very successful player in ATG: get the best pitching you can get and platoon. There are a lot of cards in ATG and you can guys that crush each side of the plate. By platooning you can get a very powerful offense.
4. Defense
30 out of the 108 chances on your pitcher's card are actually based on your defense. 7 SS, 6 2b, 3 3b, 2 1b, 3 c, 2 lf, 3cf, 2 rf, 2 p. Your defensive playere are rated 1-5 fielding and you get throwing ratings for the outfield. As a general rule you have to be at least wary of having less than a 1 or 2 at SS, 2b or CF. And you could use defense as a strategy, too. Say you have a pitcher's park that does not give up BP singles or BP homeruns. Then you get a great pitching staff...and then you get a great defense. You may have really starved the other team of runners; this could give you an advantage.
Anyway, there all kinds of strategies. I suspect the easiest one to make you competitive is get an extreme power park, load up on power/on-base guys ,(think money ball), get a number of platoons with each side having power, and get good defense up the middle. I think you'll do fine doing something like that. My lone ATG team (Until that team I exclusively played 20XX) is down below and I was decent (not great), to give you some idea of what such a team would look like.
Good luck!
https://onlinegames.strat-o-matic.com/team/1538915