I have a "Pistol Grip" BLR chambered in 358win,..and a "Straight Grip" Model 81 BLR chambered in 284win,..both are very excellent rifles,..I can't find a thing I don't like about them,..they are accurate as bolt action rifles,.. short and quick handling,.. action is smooth as butter,.. quick loading/unloading,.. light and nice to carry,....IMO, they are one of the best all around rifles out there. However,.. if I were you I would get the BLR in "short action", IMO having a BLR in long action kind of defeats the purpose of having a lever action. There is a considerable difference between the SA and LA,..
Short standard cal action eg: 308win,..length of pull = 13 3/4"...barrel length = 20"...overall length = 40" ...weight = 6lbs 8oz
Short magnum action eg: 300wsm,...LOP = 13 3/4,... BBL = 22" ...OAL = 42" ...weight = 6lbs 12oz
Long standard cal action eg: 30-06sprg,...LOP 14 1/4,... BBL = 22" ...OAL 43" ...weight = 7lbs 4oz
Long magnum action eg: 300 win mag,...LOP 14 1/4,... BBL = 24" ...OAL 45" ...weight = 7lbs 12oz
As for the trigger being a little heavy on them,...I don't see a problem, they aren't as bad as some people make them out to be,..I can shoot moa groups with both of mine,..the BLR is not designed to be a bench rest rifle, it is a very handy effective hunting rifle. As for the magazine,.. I have never had any problem with either of mine falling out on its own, the release button is tucked up past flush in the bottom of the receiver/forend, and the only way I see it coming unlatched is if you do it with your finger.
If you handload, my suggestion would be the 358win,....if you don't handload, my suggestion would be 308win over the 30-06. As already stated by other posters, the difference between 308 and 30-06 is little to none with 150 to 180gr bullets,...the short action in the BLR is the way to go. If you need more performance than the 308 can provide I would go with the 300wsm. Don't get me wrong, I love my 30-06s, but I think the long action is better left for the bolt guns.
I don't know if you are familiar with the highly underrated, unnoticed 358 Winchester, but it is one great old thumper, good for everything from mice to moose,...do some google searching on the 358 and I think you will be impressed,..here as a link to a good read about the BLR and the 358win,....
http://www.gunblast.com/Browning-BLR358.htm
Go get a BLR,...you won't regret it.