TL;DR: 12/2 on a 20A breaker for the branch circuit, 14/3 for the motor connections, but pay attention to the wiring details to the motors
The easy TL;DR for this is that you can use 12/2 for the branch circuit run and 14/3 from the VFDs to the motors, with a 20A breaker at the panel and 20A Class J fuses in the local disconnect (a Siemens HF221N with the load base configured for Class J fuses will do nicely there). However, the path there is not a simple application of branch circuit rules, but takes us on a winding tour of NEC Article 430, with a detour into cable types and ground imbalances along the way.
We start with the 430.6(A)(1) (Table 430.250) FLA for a 1HP, 3phase, 230V motor, namely 4.2A. We also know that the chosen drive's own specifications max out at 9.2A of input current at full load, and that a 12AWG copper conductor is rated for 25A at 75°C despite normally being limited to 20A by the NEC 240.4(D) small conductor rules.
With these numbers in hand, we head for NEC 430.122 to start sizing our conductors, since we are in a VFD application. This requires us to use the VFD nameplate input current as our baseline for conductor sizing, not the motor table FLA, because drive losses and the 1Φ/3Φ conversion would throw us off otherwise. From there, we apply NEC 430.24 to get us 9.2A * 1.25 + 9.2A (125% of the largest motor load + the remaining motor load, in this case), which comes out to 20.45A overall, well within the 25A permitted by Table 310.16 for a 12AWG wire landed on 60°/75°C terminations.
From there, we move onto the branch circuit overcurrent protection, which is a two-part affair, due to how your drives are listed. First off, we have to size both parts of this, which takes us to NEC 430.131 since we have multiple drives on the same circuit. However, we can't use the motor full-load current straight-up as the NEC specifies here because we have a single phase input to these drives. Instead, we either multiply our 4.2A full-load current by √3 to get us a 7.3A equivalent single phase full load current, or use the Table 430.248 value for a single phase, 1HP, 230V motor, namely 8A.
Either way, we then move over to NEC 430.53 on motor group installations, as specified by NEC 430.131. Since our branch circuit is larger than 15A, NEC 430.53(A) does not apply to us, so we move down to NEC 430.53(B), which lets us stack multiple larger motors on a single circuit provided they are individually protected against overload (in your case, this is a matter of programming the drives correctly), the breaker can provide branch-circuit protection to the smallest motor as per NEC 430.52, and the breaker will not trip under the most severe normal service conditions encountered. Since the last point can be handled by having the drives throttle the motors appropriately, we can treat the smallest motor as a 7.3A load, multiply by the 250% factor given by Table 430.52 for an inverse time breaker, and then round up to the next higher breaker size as per 430.52(C)(1) Exception 1, which gets us our 20A breaker.
However, while that 20A breaker is sufficient to protect the motor branch circuit itself, the drives require a bit more help. In particular, according to Table B3 on page 133 of your drive's manual, the WEG CFW300 family of drives is only Listed for use with Class J fuses or for WEG's self-protected combination starters, not for being protected by arbitrary North American inverse time circuit breakers. Hence, we need to incorporate a set of Class J fuses into this design as additional overcurrent protection; fortunately, your drive supports a maximum fuse rating of 20A, so we don't have to worry too much about trying to juggle sizing here.
Finally, we run 14/3 from the drives to the motors, since we can't run anything smaller without running afoul of the small-conductor provisions in NEC 430.22. The cable type for this run, though, matters, as discussed below.
If you've read this far, or skipped to here...
Now that we know our wire and overcurrent protection device sizes, and have our local disconnect in place as per point (c) in the Exception to NEC 430.112 that lets us have one disconnecting means for two co-located motors, we can focus on wiring things up. The run from the disconnect switch to the VFD cabinet will use more 12/2 MC; however, the VFDs you chose may or may not accept 12AWG for their input conductors. If that's the case (I can't tell from the manual whether it is or not), then you'll have to run 14AWG pigtails from the drives to the incoming power feed from the disconnect, which is permitted by the NEC 430.53(D) point 2 tap rule as we're staying within a single cabinet (hence, not exposed to physical damage) and not exceeding the 25' limitation imposed there.
On the output side, though, things get tricky. Ordinary MC cable is not the greatest choice for a VFD output since the way the grounding wire is cabled in causes a geometric imbalance in the currents flowing in the cable, which causes imperfect magnetic field cancellation and ensuing EM noise radiation from the switching frequencies of the VFD. The proper cable to use would be what's known as a MC-HL (Hazardous Location) cable, as these cables have special armor that can serve as a grounding means all on its own as well as tripartite grounding conductors within the cable that ensure symmetrical current flow under all conditions.
However, those cables can be somewhat hard to source (some online suppliers will sell them by the foot) and install (due to having that special armor), so regular 14/3 MC is more-or-less an acceptable substitute in an application like this. Either way, you'll want to use snap-on type fittings (Arlington 38900ST or equivalent), as these provide a good 360° grounding path from the cable armor to the enclosure at each end. You'll also want to use a metal cabinet/enclosure for your drives, in order to provide EM shielding, and you may wish to use the EMI filter kits WEG offers as well.
