take your pick of variables

Momentum is simply related to synchrony-free proper velocity w ≡ δx/δτ = γv and frame-invariant mass m, as well as to frame-variant mass m' ≡ γm and synchrony-dependent coordinate-velocity v ≡ δx/δt, by

where x is map-position, t is map-time, τ is proper-time on the traveler's clock, and Lorentz-factor γ ≡ δt/δτ from the metric. So far so good, except for the frame and synchrony dependence of m' and v which make them more difficult to measure and/or discuss from different points of view.

However in terms of the frame-variant (momentum rate-of-change) net-force variable Σ_if_i ≡ f_net = δp/δt which is directly connected to the causes of motion, it turns out that:

Hence frame-invariant mass times the rate of proper-velocity change equals the 3-vector rate of momentum change at any speed. If you want to preserve the familiar Newtonian relationships p = mv and f_net = m δv/δt at high speed, then using frame-invariant mass m and synchrony-free proper velocity w is the way to go. In particular the frame-variant mass m' fails to track momentum changes as a 3-vector velocity derivative.

At high speeds, the relationship of momentum-change rate to both frame-invariant proper (felt) acceleration α and frame-variant coordinate acceleration a ≡ δv/δt is more complicated, namely:

Hence synchrony and frame dependent coordinate velocity v and acceleration a relate to rates of momentum change through frame-invariant mass m, but not via a simple velocity derivative and with no simplification coming from use of frame-variant mass m' = γm. At high speeds and in curved spacetimes, the local "traveler-point variables": frame-invariant proper (traveler) time τ, synchrony-free proper velocity w (map-distance per unit traveler time) and proper acceleration α (with its frame-invariant magnitude) are of course even easier to use in conversations that involve more than one perspective.

In particular use of these local traveler-point variables (with but one metric-based definition of simultaneity to worry about) allows kids to solve relativistic acceleration problems not accessible to special relativity, without requiring the more abstract tools of general relativity (like the Rindler metric). How cool is that?

More generally, traveler-point variables are local (and minimally frame-variant) 3-vectors and scalars with ordinary units (e.g. meters, seconds, etc.) because the global 4-vector symmetry is locally a (3+1}-vector symmetry instead. That's also why our everyday unit systems, plus position/time and momentum/energy measuring tools, follow the (3+1) breakdown as well.