Once I have reached an AP of 100km I switch on the OMS engines and rotate the shuttle upright to make control input easier. Once the SRB's have gone you have more control but again I am leaving everything except pitch alone, the lighter the tank gets the twitchier it will be. Pull back slightly straight away and slowly try and nudge it towards 45' by the time the SRB's are about exhausted, the closer they are to spent the smaller your adjustments should be as they are closer to overwhelming the SSME's I am not making any other adjustments here except nudging the pitch, and I advise you to do the same, deviating will result in instability.
In the video below you can see me pilot the Space shuttle with an 18t cargo to an ~100km orbit and return. There are two example craft, the Shuttle can take a 18t+ payload to 100km+ and the SLS can take a 70t+ payload to 100km+, that should make them quite flexible for most needs. If you have Firespitter you can also have orange tanks. But that also makes a quite capable SLS possible. The engines have been re-balanced for the Shuttle as that is the least dynamically stable of the two designs. Using Module Manager by duplicates several parts, and then resizes and enhances them. The purpose of this mod is to make building a stock size Space Shuttle and SLS easier, with less parts and without using much more memory.