The way I'd do it for Fighters, if I were going this route, would be to give them Light and Medium Armour at 1st level, then a choice between shields or Heavy armour at 2nd, and whichever was left at 3rd.
It's a bit slow because it means that classic knight must wait 3rd level, but can be done.
I am not sure this is really needed however, IMHO there is hardly a problem with getting all armor prof at once because anyway (1) almost all class already get some armor prof anyway, and (2) the max Dex limit means that for a lot of characters Heavy or even Medium armor prof is useless.
For weapons, give them all simple weapons at 1st level, and divide military weapons into three groups, of which they choose one each at 1st, 2nd and 3rd level.
I like this less, because if the purpose is avoiding dipping for the proficiencies, then this doesn't prevent dipping. For most characters 1/3 of martial weapons is plenty, since they'll just pick the favourite type and stick to it.
Very large weapon profs are useful only (1) for beginners and the undecided, or (2) in campaigns where magic weapons are so many that it's good to be able to switch them often.
So then to avoid dipping successfully you must give at max 1-2 weapon profs, which is quite sad for the regular Fighter player...
All in all, I don't think the issue of proficiency-dipping is so important in practice, that it justifies complicating the system or (worse) penalize single class characters. If it was for me, I'd probably just handwave full proficiencies at 1st level.
Personally, I'm not too bothered if a character who starts out as something other than a Fighter gets fewer weapon and armour proficiencies - a similar system worked well in Star Wars Saga Edition, and this way some of those weapon and armour proficiencies in the new mega-feats might actually be useful.
The only negative IMO is that when you create a character starting at higher level, it does suck if you discover later that if you took the levels in your classes in the opposite order you would have gotten some better results.