When I play USF, I rely heavily on the cpt to supervise and get stuff out fast. The idea is, USF can gain a significant advantage by dominating the early game. This sometimes works, sometimes not. Does anyone else here think that way, or is it generally better to go lt first ? The only think I can think of is having access to HMG and light armour earlier I guess, but then being constrained by "regular time", not "accelerated time".
Its all come to snowballing effect. With lieutenant first you must snowball thus play aggressively. With captain you can play more passive. As said before it depends on the map and faction you're facing.
Lieutenant is better vs OKW because they rely a lot on blobbing to overthrow you from a place. The HMG is nice to hold off and support your riflement in this purpose. HMG tend to be less effective vs grenadiers with their long range weapon and grenade and M20 and Stuart are more subject to be snared. The stuart is also better to poke OKW AAHT or Luch than US AAHT.
Captain is better vs Ostheer because as you said they get their medium first so an Atgun is always welcome to temporize till your sherman roll in and AAHT is definitively better vs the 222 and to suppress from afar grens/pzgrens. The pakH is also a good investment vs Ostheer more static way of playing.
Now if you're confident in your micro and by this I mean Light vehicle micro, you must pick the lieutenant first. A well use M20 is an absolute nightmare to deal with as Ostheer, once vetted you'll pick regularly and fast 1 model from 4men squad grens or pzgren and then let your rifle finish the job forcing early retreat. The M20 gives you free tech smoke and is best to flank lonely HMG. Then The stuart is just there to assist and keep the 222 away.
With this strat you should be bleeding your opponent hard enough to delay him in his tech to his first Pz4.
Evidently, to gain confidence in microing your LVs, you must learn it first the hard way, no other solutions.