I am not a fan of omni antennas for the current LEO satellites. The eggbeater or moxons are marginal performers at best.
Short, quality feedlines and RX preamps are good ways to minimize ineffectiveness of omnis but there's no silver bullet.
If you have no other choice but omnis, you may find yourself limited to certain satellites and certain passes. SO-50, for example, is not going to be favorable. Compensating for lack of hearing ability by running full power won't make you many friends.
Working satellites on an almost daily basis, one can often identify an eggbeater or omni user by their inability to hear a very strong signal from the satellite.
As previously mentioned, a set of small yagis at a fixed elevation with an azimuth rotor will yield far better results. The trick is not using longer, high-gain yagis. You'll have more beam width with smaller ones. Considering what many stations achieve with an Arrow or Elk antenna (7,000+ km contacts,) bigger isn't always better.
Omnis are okay as long as you understand the shortcomings.
73 Clayton W5PFG