For Push-Pull EL84 output transformers, anything from 6k to 10k should work fine. Many 100 watt transformers fall into the 6K range and believe it or not, will work great with EL84's. Transformers for 6L6's in the 50 watt range fall around 3-5K and may still work, but there could be some attenuation. To be more concise, as long as the transformer lies between 6K and 10K regardless of what it was used with before, should work great.
To answer your second question, chances are that if an amplifier had solid-state rectification, there will be no 5v filament windings for a tube rectifier on the power transformer. You can do the opposite and use solid-state rectification in place of tube rectification. The high voltage will be higher, so the amplifier circuit itself will have to be made around that fact.
Does it make a difference to the output transformers whether the circuit is using tube or SS rectification? It can, but there are ways of dealing with it and it won't make any difference to you. I've worked with scores of varying transformer scenarios and never had a problem that couldn't be satisfactorily resolved.
Are you asking which sounds better: Tube rectifiers or SS diodes? I realize that this is a Ford vs Chevy argument to many, but the answer is concrete to me. Tube rectifiers are great for amps under 30 watts/channel. Above that, SS diodes do a much better job because they will not allow the high voltage to sag and color the audio. A side note: What IF someone wanted the audio to be colored a certain way? Then I must choose the proper parts to fit the job at hand. This is a great topic and I hope others join in.