^ I did a modified hunter clip for my mare's first in my ownership. I left legs and ears on, and took everything else off. I'd have clipped her ears out too if she'd let me. Legs were left on in the hope that the fluff would offer her a little more protection from injury as she is highly accident prone.
It did not.
A full clip is the easiest if you're not confident making neat lines with the clippers, but also requires the heaviest blanketing (and often paddock boots to keep the legs warm, and a hood for the face!). A chaser or trace is a nice middle-of-the-road clip but that's a lot of lines to try to get looking even. You can mark your lines with chalk or duct tape to get them even before you clip if you want to make it easier on yourself.
If YOU are going to clip your horse and it's your first time, remember:
TAKE YOUR TIME. The more time you take, the better your clip is likely to be.
Long smooth strokes leave fewer clipper lines.
Keep the blade flat against the skin, you'll get the smoothest clip.
Desensitise the horse to the clippers before trying to clip or you'll never get a good clip job done.
Sedate if you can't desensitise. The stiller your horse stands, the easier it will be to get a nice clip done.
If your horse has never had the face done before, leave the face alone. Trust me.
Leaving hair on under the saddle can make them less likely to be frisky after a fresh clip. Ask me how I know.
Check your clippers often against the back of your hand for overheating. Spare blades make it easy to keep going - you just swap the blades over. Sometimes the motor itself gets too hot, and will heat the blades up REALLY fast, so a lot of professionals clipping multiple horses will also have a spare set of clippers to swap out every 1 to 2 horses.
If your blades stop cutting, check the tension, then check the sharpness.
Start with an EXTREMELY clean horse and sharp blades. Clean to the skin, not a speck of dust. Wash, dry, wash again, dry again. Your blades will stay sharper for longer if they're not fighting dirt and dander.
The cleaner your horse and the sharper the blades, the less clipper lines you will leave.