Hands:
Possibly the bars are too low.
Possibly you keep your arms too stiff, although that usually hurts the elbows or shoulders.
Possibly some thicker h'bar tape will solve the problem.
Possibly gloves - although my hands hurt if I wear cycling gloves, and my elbows and shoulders hurt if I don't.
Seat:
Saddles are very personal; what works for one person may not work for another. A lot of shops give you 30 day trials - that's std for Specialized, for example. There's a place that offers 6 month trials for leather saddles. I think your best bet is to choose between:
1) pick up used saddles on CL and sell what doesn't work out for you, and
2) find a shop that will let you try the saddles out for a good period.
Bikenashbar offers basically an unlimited trial, but they're mail/web order, and if you do business with them, your local bike shop may not be around when you need it. Prices are great, though.
I've gone from an Avocet Touring I (no longer available) to an early Fizik Aliante to a Specialized Toupe back to the Aliante.
My belief is that a seat that makes you perch on your sit-bones is best, so I tend to look for harder saddles - i.e. least padded.
The shorts used to be wool and leather chamois. The purpose wasn't to cushion your butt; it was to absorb the sweat.
You know the usual SI advice about looks. The shorts will probably make riding easier and healthier for you. That's the only thing that counts, and I urge you to try 'em out.
I look awful in the shorts, too, BTW, but I couldn't do 20 miles without something like them, and my goal is 70 on my next birthday. So I wear the shorts. After all, other cyclists only have to look at me until they pass me.