Hello tot ou tard,
Am I right that you have two issues? Tuning problem and the question if to use a floating or fixed system? Well, the fix tremolo bridge for example on a vintage strat always leads to a warmer tone. Let us take the beloved position between middle and neck PU. Sounds woodier and more hybrid with a fixed tremolo, therfore playing a floating one gives you more warmth or ket us say a more civilized tone in such a position. If you do not use the tremolo then fix it. Of course the guitar will stay better in tune then, but bear in mind, the differnces are marginal! I have both options and luckily my strats are perfectly set up, so to be honest, I have no tuning problem also if going wild with my guitars. Let your first issu be the tone - only your flavour counts. Try both options. Then get an explanation on how to set up a vintage tremolo system or bring your guitar to someone who really knows. Measure the neck, think of the "step" like system to set it up and there you go.....