It doesn't sound stupid. I love trying out things that I've seen on TV. Ok, I'll list as many types of turns as I can think of (I don't know how many of them you can do - if there's any you don't recognise, your coach can explain them to you):
2 foot turns
Three turns (FO, FI, BO, BI)
Double 3 turns (Forward then backward, or vice versa)
Twizzles
Brackets
Counters
Rockers
Mohawks (forward open & closed, backward)
Choctaws (all the different types)
Chasses
Closed chasses
You can also incorporate:
Hops (e.g bunny hops, side-hops, mazurkas, ballet jumps, etc)
Small jumps (e.g. stag jumps, split jumps, half jumps)
Positions (e.g depending on how flexible you are, you could hit a couple of nice positions like kicking your leg up)
Toe steps (e.g. Yagudin's Winter SP)
Spread eagles, ina bauer positions, etc
Edge changes
And also upper body movements, to add interest, and you can also experiment with the free leg on 1 foot turns etc (e.g. where are you going to have it?)
Have you got Sasha Cohen's SP from the 02 season on video? If so, watch her circular step sequence. She has a couple of hops/small jumps in it, a Russian split jump, and at one point she swings her leg up to her face then back to the layback position. Unusual, and looks nice. Actually, watch as many step sequences as you can, they might help give you ideas.
Three patterns to choose from - straight, circular or serpentine.
One thing to add interest is to do rotations in both directions. Also, don't do it all on 2 feet. Try to get a big variety of moves in it, and relate it to the music (with timing etc). You can make sharp, staccato moves or softer, flowing moves. Or both. Depends on your music, your abilities and your preferences. Spend some time just experimenting with short sequences of things, seeing what feels good, being as imaginative as you can.
Hope that helps!