Rugs are measured from centre of chest to point of hip (where you want it to stop at the back). My 16.2 surprisingly slender clydesdale X wore the same rug as my friend's tubby Dales pony at 14.3. How they fit around the neck is the major issue - and varies on makes.

I was always happier slinging rain wet horse rather than sweat wet horse back out with a rug on. Assuming you're not clipping his back, rain is unlikely to penetrate to his skin and good rug will allow the water to evaporate. Sweat is water at the skin and will tend to chill them when they cool. Ideally of course, dry him off.

Rattling Ghosty is asking about measurement for exercise sheet though which is a bit different (it won't involve the neck/chest). My sister has just ordered a waterproof one for me for Christmas and we weren't sure either as there only seemed to be two choices on the one we were looking at (in Robinson's sale). In the end we decided they must be pony and horse and plumped for the biggest one so hope it's ok!
Ghosty I don't really like putting rugs on over wet ponies either but sometimes it can't be helped and they seem to manage ok. Making sure they have some hay so they can generate heat from inside helps them to warm up and dry off more quickly. If you are going to be coming back later (or have time to hang around for a bit) you could always put a sweat rug or waffle rug underneath the other rug for a while to help the air circulate and take up some of the water (we used to thatch with straw under a jute for same effect).

I've always measured exercise sheets the same way as normal rugs, from chest to hip, there is a handy guide here:
www.horserugsonline.co.uk/size.php

Modern rugs are breathable, they should be able to allow a certain amount of moisture to dry out so I wouldn't be too worried about putting a rug back on a wet pony. If the pony is absolutely soaking wet then you may need to use a sweat rug for a short while in the stable to soak the moisture out and then put on the turnout.

We don't use exercise sheets our horses/ponies although I may wear one on a clipped thoroughbred. I do have a hiz-viz one that we used on a heavyweight show cob a few years ago but that was more to be seen when hacking in the semi-dark rather than for rain protection.

When (not if!) our horses get wet we give them a quick towel to get the worst off and the put turnout rugs back on and out in the paddock. They will soon dry off.

We leave our turnout rugs on when they come in as well - it saves time and keeps them snug. We only take them off for an air - replaced by stable rugs - when keeping them in during the daytime for farrier, vet etc.