It seems like up to about halfway through the first season, they were very inconsistent about exactly how the transporter was activated. In The Corbomite Maneuver, Scott engages it with the slider as is seen just about the whole time in the series. But in Enemy Within and Dagger of the Mind, Scott or the chief is telling the tech on the right to energize, with it looking like the slide ris being used to 'reintergrate' the beamee. Actually, it looks like in EW that the quick repair solution changes the activation process.
And as far as the transporter itself is concerned, remember in the pilots, for the transporter console all they did was move the helm/nav console and called it the transporter. When they got the series OK, it was deemed necessary to have an actual dedicated console, as the transporter would be as important a set as any on the ship, and people would notice it being the helm console very quickly. (actually, for the series, it looks like they built an entirely new helm/nav console - or rehabbed the first one VERY extensively. Sure looks sleeker)
And I have always thought that about the 203/430 difference also - certainly Federation technology gets smaller, as ours does. Plus, perhaps, Starfleet's personnel base was bigger, too.