I'm sure you will get differing opinions on this (a lot of very good owners on this site will even say it doesn't matter what park you pick), but in my opinion the key is to do the opposite of what you are doing. Picking a neutral park and a neutral team will lead to your team rarely having a true advantage, unlike a triples team in Petco or a OBP team in Safeco (you get the idea). Since other owners are doing this, they will frequently have an advantage over you while you will never have a similar advantage over them. Even if you field what is essentially a very good team with cost effective players, you'll win less than you would have otherwise, in most cases.

Make a theme for your team and then pick the park that best fits with that theme. Any theme can win (HRs in Yankee III or Sick's, good range and great pitching in Coors, triples and good range in Mile High, etc) it's just important that you pick one.

Wait, I'm confused a little.

HR in Yankee Stadium. Okay, that makes sense. Picking a stadium to match my strengths.
Pitching in Coors.... Doesn't that directly go against your original statement?? How would pitching benefit from the hittiest park there is?

The idea would be that with above-average hitters you will already get an offensive boost in Coors, but you need way above average pitching plus a LOT Of IP since getting hit so much means throwing more pitches there.

If you are in a real pitchers park like the Astrodome, you can figure your pitchers will perform better and neither your team nor opponents will hit a lot of homers, so you can risk pitchers that are otherwise great but maybe give up some HRs in real life, but you would not want to build a power-hitting team (see Wynn, Jim re: 500 homers not hit in his career cause he played there !).

In the Polo Grounds and Fenway you will get a lot of doubles, but so will your opponents, so you want pitchers with low OAV and who don't give up many home runs, and an offense that can take advantage of that park.

Everyone has their favorites - I don't like the pitchers' parks, but no question the most successful owners here do. I like hitters' parks like the Kingdome and Tiger Stadium, but then you have to find pitchers who do NOT give up HRs - usually the deadball era ones.

Also, if your park facilitates singles, doubles and triples, but not homers and you build a team that can take advantage of that, (see the park effects data above in the screen on the page when you are drafting a team for these effects) you want good fielders, and can probably risk higher BB/9 by your pitchers but not higher OAV. And so on.

If you usually play in open leagues and aren't having the type of success you'd like, then make a change and experiment with something new. I agree with what Italy and ozo said. I also am one who believes the park you chose to play home games in CAN make a difference. Take for example Comerica. The park favors singles (i.e. getting hits in general) and triples. It suppresses home runs. Consider drafting a speedy offensive squad with players who have good 3b/100#s... compare that normalized stat to their 3b/100AB figure. You can draft pitchers with a bit higher HR/9#. Try getting some speedy triples hitters who can chase down flyballs there. In Dodger stadium (+2 for singes, but big negatives for doubles and triples), try drafting contact hitters with good 1b/100#s and fewer walks. I like a 3-1 hits vs. bb ratio for my position players there. The list goes on and on. There are a million ways to win in the SIM. I just took a team of all 2015 players to an Open League World Series (where I lost). It was fun to see them compete well against the cookies and dead ball pitchers.

italyprof got at what I meant but we do have one difference of opinion in that I'm not a big believer that parks like Coors and Mile High make you need that many more IP than other parks as long as you have good defense/range and low bb/9. You may need some more, but I believe the effect is less than most people think.

The key is to look at the team you make and think "where will this team have an advantage over the average team in this league?" In Coors, other teams will be exposed if they don't have great pitching and defense in the same way that in Yankee III, teams without HR hitters and/or with pitchers who have bad hr/9 will be exposed, etc.