Detachable sleeves - nononononono - not only a re-enactorism, a fecking dangerous re-enactorism, as already pointed out.
You need proper sewn in sleeves, cut so that they move.
Do not use ovenglove wadding - it's made to trap heat one way or the other and you'll bake. Look at quilt wadding (the proper kind, not the horrid polyester stuff). It depends a lot on the wadding, but go for a cotton one, and you'll likely need 8 - 14 layers depending on the thickness you want, plus the fabric layers.
Thickness, depends what you're doing - most semi contact anything up to about 0.5" is fine - full contact then more like 0.75 to an inch. Some blows will get through no matter how well padded you are. You don't want bruises, you shouldn't be on the field (my personal opinion
).
If you're wearing plate over it then you'll need little or no padding. If you're wearing something more flexible (like mail or coat of plates type stuff) then you'll need more padding. So for crecy era, that at least means slightly thicker padding in the body (as described above).
How thickly you pad the arms depends on what you have over the sleeves - with plate they need to be pretty much unpadded and tight and well fitting - with less plate ( or other solid stuff) they need to be thicker.
Remember that if you have solid protection at one point on the arm, but not another, you can adjust the actual padding to match. Also remember that you need to be able to move your arms still. Same goes if you choose to make apdded hose.
You're not making an 'arming jack', because there's no such thing - it's a term only used by re-enactors who know little or nothing about padding.
There's little difference between a gambeson and an acheton (some say that one is under armour and one over, but the distinction wasn't really made at the time - it's a later hand over from those dear victorian dress historians (the ones who invented 'ring mail'). You culd also throw in jupon, jack, coat armour, arming doublet, etc, etc.
Actually, come to think of it, mid fourteenth century - you're coming into the period when you should have two laers of padding - one over the armour and one under it it.
Fastening - you can use buckles, though they're questionable in terms of accuracy. Nige is right - hooks and eyes or points. hooks and eyes have the speed advantage (putting on and taking off), points have the secureness factor (unless the point snaps they'll stay fastened). obviously points do snap from time to time, and you'll need to get proper arming points.
If you want points you'll obviously need holes in the padding - for hooks and eyes you just need to sew them on (using buttonhole stitch for strength). To stop them popping you alternate them (hook, eye, hook, eye, etc) - and get proper sized ones, and don't go with modern fur hooks and eyes, (the fabric covered ones) cos they're not strong enough, they're brittle, and they snap.
And a port piece under the gap is a must. I lightly pad mine.
"What a lovely hat! But may I make one teensy suggestion? If it blows off, don't chase it."
Miss Piggy
RIP Edward the avatar cat.
I also suspect that half of it is just plain wrong, so I could really do with some helpful advice:
)...not quite 0.4" thick. I'll give that a go and see how it performs.