PorterGuy - lots of good advice above, but here's a couple more things to think about.
Have Orbit up on one of your MFD's, and have the surface HUD up in the main window. You are looking to fly East ideally, to gain the maximum benefit of the spin of the Earth. (If you are going to a specific place - e.g. Mir or ISS - then your heading may vary, but just to get into a free orbit, then head east). If you are on a fuel budget (read: realistic flight in one of the vehicles you mentioned), then you want to get up above 10km on quite a sharp angle (e.g. 70 degrees), then gradually flatten it out to horizontal by say 50km.
On the orbit display - click DSP so the left side says PeA and ApA (altitudes) rather than PeR and ApR (radius distance from center of Earth). Watch how Altitude (ALT) goes up relative to ApA (your Apoapsis Altitude - i.e. top of the curve of your ballistic trajectory or orbit). As your speed picks up past 6500 m/s you'll start to see ApA grow bigger than ALT. This means you are starting to overcome gravity with the centrifugal force from your horizontal velocity (i.e. stone on a rope starting to pull the rope taught as it picks up speed around the circle). When you hit the magic speed (around 7500 m/s, you will see ApA rapidly increase to say 200-250 km, despite your Alt being say 80 km). This is a perfect time for Main Engine Cut Off (MECO), and let the ship cruise up to the Apoapsis (watch ApT trend down to zero on Orbit MFD).
At this point, you need to do one more thing to complete your objective of getting to orbit. At ApT = 100-200 secs (e.g. 180), hit Prograde autopilot. At ApT of a few seconds (depending on your rocket power - you need to figure this out, but say 10-15 secs for a realistic engine and 5 secs for a DGIV or XR-series ship), hit the throttle again for a short burn of say 10-30 secs, to raise your Periapsis up to your Apoapsis. (Watch PeA coming up to the same value as ApA, and Eccentricity (Ecc) going down to 0.000). As you get close, you can use your forward and reverse translation thrusters to get to the elusive Ecc = 0.000, or perfect circular orbit.
Hit F1 and admire your handiwork! You'll be in orbit.
p.s. Don't feel shy about using a DG or DGIV or an XR-2 to try this stuff out. The overpowered engines are ideal to get a feel for the orbital mechanics first, and give you much more performance margin to play around than say the Shuttle's engines.