Without replacing the bridge (or at least the saddles), the only advice I can give on setting it up is to make sure that the top of each saddle is level and that both of each saddle's screws are touching the base plate. It only takes a small difference in saddle angle and screw height before one of those screws is up in the air and the saddle is only resting on one screw. If the other screw is only slightly above the bass plate, then it may well vibrate against it and buzz.
If you've got a lot of saddle screw poking up above the saddle, so that they dig into your hand, then you can either a) get a small hacksaw and cut a few mm of the bottom of the screws (I'd leave the hex hole end untouched), then use a file to smooth off the edges and add a bit of a point to them or b) look for shorter replacement screws from an eBay seller (though you'd have to guess at the screw size, though most Asian made saddles will have the same size and thread).
I tend to replace cheap alloy saddles on my (or friends) guitars with Graphtec ones as they do cut down on string friction a lot, and I find that their screws aren't overlong to begin with, so you don't get anything poking in your hand. The all-black ones are the cheapest, though you can get steel versions with just an insert of the slippery black material at twice the price. There are also good steel saddle replacements out there. But you need to measure the string spacing of the saddle to make sure you order the right size. Normally this will be the narrowest if two options are given, as most Asian and Mexican built guitars have a slightly narrower string spacing to US made guitars.
This is where getting a cheap digital vernier calliper pays dividends. I bought one for around A$20 from eBay and it is surprisingly accurate and I find myself using it a lot to check measurements.