Decimating physics data
This is a really very nice applied signal processing question. Unfortunately your lack of DSP and physics expertise, builds some barriers on the way of your understanding. Hopefully this answer helps to tunnel through.

Now, your first question is about downsampling a discrete time signal. In fact there are already plenty of such questions here under the title of interpolators, downsampling etc. These are already answered with great detail. You better make a search on the site for more detailed answers but here once more I'll give a brief reply. 

In downsampling a discrete-time signal (say from 360 hz to 60 hz in your case, by a facttor 6) the most critical thing to consider is the Spectral Utilisation of the original (360 Hz) signal. Based on Shannon-Nyquist sampling theorem criteria, this signal is assumed to contain meaningful (non-trivial) information in the band of frequencies 0 to 180 hz. However for many applications the frequency band of interest within the say 0-180 hz range will be a much smaller band, say for example from 0-20 hz. In such a case, the original signal is said to be "oversampled" (by a factor of 9 in this case). When a signal is oversampled by a factor of say M, then it is somewhat acceptable to discard every (M-1) samples and use the Mth one to represent the information content of the original signal without loss (except at the higher end of the band which gets to limit of aliasing). But this will/may produce some noise due to aliasing being on the very edge of it. 

There won't be any aliasing, as long as the out-of-interest frequency band in the original signal contains no energy. In order to guarantee this condition of zero energy in the out of interest band, it is required to filter out those out of interest bands by a suitable filter of sufficient quality, before decimating the signal. 

The quality of such a filter depends on, therefore, i-the spectral distribution of the original signal, ii-band of interest, iii-downsampling factor and other requirements such as real time processing or offline, accuracy, CPU power etc.

In your case, the answer lies in the following: the best downsampler should produce the most accurate representation of the band of interest signals and reject any irrelevant information for your steering hardware to process.

The short answer is this: as long as your system is configured to use 60 hz information (30 hz band) for the force-feedback processing, it seems that (and from my experience with mechanical acceleration signals, it is indeed so) this band of signals is adequate to represent average mechanical control. (as long as I can remember, most mechanical acceleration sensors do use at most a band of a few hundred hz). So just use a simple low-pass filter of cutoff frequency at pi/6 for better performance.

The second questions simply asks which is better to choose i-filtering 360hz into 20hz or ii-60 hz into 20 hz. The answer is the latter. It will be a much shorter filter to apply, and the transition band would also be easier.

When the latency of a few samples becomes so critical as in your example of real time forced-feedback control of a physical simulator, then high accuracy filters becomes impractical to use. May be you should completely discard using any filters at all, as you have pointed out the physical limitations of the wheel mechanics already prevents bulding of responses faster than 20 hz...