It depends which circuit you're going to, but F1 tends to have very large runoff area's, so the crowd is usually not that close to the action, so a 300mm lens might not give you what you want, even on a 1.6x crop sensor and depends where you are, safety fences have a great tendency to get in the way of your shots.
Personally It depends what subject you are photographing, what speed the subject is travelling at, what lens your are using and getting the right shutter speed / aperture to match to create the right motion blur rather than VR OS IS etc. Correct camera settings and a smooth pan get you the shots.
Shutter speeds of 1/30 1/60 or even 1/125 aren't easy to get right. So apply the 1 over focal length rule explained below to get an idea of somewhere better to start.
A common rule of thumb for estimating how fast the exposure needs to be for a given focal length is the one over focal length rule. This states that for a 35 mm camera, the exposure time needs to be at least as fast as one over the focal length in seconds. In other words, when using a 200 mm focal length on a 35 mm camera, the exposure time needs to be at least 1/200 seconds-- otherwise blurring may be hard to avoid. Keep in mind that this rule is just for rough guidance; some may be able to hand hold a shot for much longer or shorter times than this rule estimates. So for users of digital cameras with cropped sensors, one needs to convert into a 35 mm equivalent focal length, eg 200*1.6 (crop) = 1/320 sec
That will help with setting up the right shutter settings to start with, you can get more adventurous later.
Now, Panning is a technique which requires mastering over time, its not something that you can instantly do and repeat. It require training you body to become familiar with the motion, thus it become almost automatic. What this will achieve is a smooth pan, something that is not easy to master.
Pick up the subject early, focus and pan with the subject, take them image when subject fills 2/3 of the frame, continue the pan after the shot, try and avoid stopping the pan or jerking at the edge will also aid in good results.
You are able to capture pans at slower shutter speeds, but to get everything right in the shot takes practice and a very smooth pan movement, taken at 1/100sec, but generally, I'm taking shots at 1/200 or 1/320 sec because of the speed of the bikes and slightly slower for cars....
for F1 cars, the shutter speeds are going to be higher, but it depends on what the cars doing.
1/100 sec
1/320 sec
or even 1/640 sec, but still generate motion blur
300mm f2.8 + 2x TC @ 1/800 sec
Feet position is important to give you a base from which to pan you body, as describe above, you then need to pick the action up early, panning with the on coming bike/car, then when it fills 2/3 screen start to take your 2 -3 images, recompose and take the next shots, remembering to continue the motion after taking the shots, that's also very important.......
Fire single shots not a burst, bursts are a waste of time for a plain old panning shot. Yes you might miss the moment when Elvis and ET climb out the sun roof and roof surf around the track to the sound of the Beach Boys, but... Concentrate on getting your timing right.
Don't shoot into the sun. That amazing corner you (and everyone else with a camera) has discovered where the cars/bikes come inches away from your face is worthless if you are shooting into the sun. Try to work out if/when the sun will have moved off and come back then.
If it is a bright sunny day, consider using a 1 or 2 stop ND filter to get the shutter speed down. Not a problem normally at 1/250th, but as you slow it down you will have problems.
Slow(ish) pans don't work if the vehicle is not on smooth ground. Its generally rubbish for non-tarmac racing as the bumps blur the subject.
Practice. Lots. Post your results up in the motorsport section on here and let everyone else give you some help - the motorsport section is pretty friendly!
Peter