So there's no perfect or universal answer to this question and it depends on your goals and constraints (e.g. short calculation time; ability to extrapolate in truncation error; high precision; limited resources; etc.) and it very much depends on the specific system you are studying.
However, for the easiest and most natural case for DMRG - that of a gapped, finite-size system with open boundaries - the most usual and recommended approach is to use a small to very small cutoff (so ranging from 1E-5 down to 1E-12) throughout and raise M from a rather tiny value like 10 exponentially quickly up to the final large value you need to get high accuracy. So a common thing I do is to just set the cutoff to 1E-10, say, and then raise M according to a sequence like 10,20,40,80,160,320,640.
The main point of using this sequence is that DMRG typically converges exponentially quickly in the number of sweeps for gapped systems with local Hamiltonians.
Another case is when you want to extrapolate in truncation or more generally use information from intermediate sweeps. Then you want to make sure the MPS is fairly well converge for each M value you visit. So a common approach here is to do the same M twice:
10,10,20,20,40,40,80,80,160,160,...etc and use the value of the energy, say, coming from the second sweep at each M value.
For very tough to converge systems there are additional things you can do. For the quasi-continuum systems we've studied a lot over the last few years, we often do many sweeps (like 100 sweeps, say) at rather small M values < 100 and then only raise M to large values after the main properties of the wavefunction like the density of electrons look reasonable. The last handful of sweeps at larger M build in the proper electron correlations needed to get very accurate properties.
Of course turning on the noise term is very important for tough to converge systems, especially when you are conserving quantum numbers.
So those are some partial answers but really the choices depend a lot on the specifics of your system.
My main piece of advice would be to do measurements of not just the energy but many other local properties of your system (magnetization at each site; density at each site; etc.) and plot these quantities after each sweep. This way you can start to build up an intuition for your system and get some idea about if your sweeping parameters make sense (like if your wavefunction is very far away from the expected physics and changing very slowly sweep-to-sweep & if there are many small energy scales in the Hamiltonian then try doing a huge number of low accuracy DMRG sweeps).
Plotting and experimenting is very important. I don't think there is a one-size-fits-all or black-box solution when it comes to best practices for DMRG.
Hope that helps -