Do I need a heavy or can I get by with a med. hvy? No grass etc. For 3/8 and 1/2  oz. jigs. 

You should be fine with a MH.

for the size you mention I would use a MH for sure. Just make sure it a St. Croix Avid

8-) ;D

If you're going to use a MH, I would suggest using braid. Even with moderate to little cover, it will increase the sensitivity A LOT.

I would go with a 7+ foot MH stick for a open water light/no cover jig rod. With not going over 1/2oz jigs MH is plenty of rod and its what I would use, I would rather use the lightest power rod I can and still be fully in control of the fish. I like using a slightly lighter rod you will have more feel of what the lure is doing and as im sure you know thats important when fishing jigs. I will sometimes fish a MH rod when flipping and pitching grass lines and scattered grass. one of my FAV jig rods in my Steez 7 foot MH (thats why I own 4 lol). dont feel like you need a Heavy action rod just because you are fishing a lure that most say you need a heavy rod to fish. if you are around cover then sure a H to XH rod will help you land fish I use my 7'1 Steez compile-X and 8' Compile-X only when jigging in heavy cover. the one thing that I will say is that if you are going to use a MH rod for jigs it NEEDS to be 7 feet or more.

If you're going to use a MH, I would suggest using braid. Even with moderate to little cover, it will increase the sensitivity A LOT.

I agree with using braid to but I would use braid to a FC leader. I use Hollow braid and make a top shot rig with FC leader about 12-14 feet of Megabass Dragon call FC.. Or I use a shorter leader of FC with Daiwa Sumari braid joined VIA a Uni to Uni knot. this is very important if fishing around rocks or timber.

I use a 7'mh and 7' h rod for pitching jigs and texas rigs and they both work great!

Personally, I prefer a heavy action for my jigs and and MH for my texas rigged baits.  But, it also depends on which brand of rods you're looking at.  Some heavy actions are more like a MH in another brand.  For instance, my Powell 704C that I use for jigs feels like a lot of medium heavy rods.  I would compare it to a MH St. Croix Avid. 

Either way, I go with fluorocarbon vs. braid for sensitivity and invisibility in more open and clear water, braid or braid with fluoro leader for stained or dirtier water.

Also, I like extra fast tips for jigs with fluoro - just a "regular" fast action is fine and probably even better for braid. 

Just my .02!   

I think it really depends on the brand you are looking for.