OnAim: The differences in the forearms stocks for the BLRs is basically cosmetic - all four of my BLRs are quite accurate despite having the barrel band, and, in fact, the band really doesn't contact the barrel at all.
The lack of sling swivel studs on the straight stock version is not an issue for me - I have hunted with BLRs for 26 years and have only used a sling on one once, when, to the dismay of some of my acquaintences, I took my 7mm-08 BLR with a 4X scope to Wyoming for a pronghorn antelope hunt (it did just fine). And you can easily add some if you decide you want them.
I have never had to disassemble the action for a cleaning and would highly suggest that you not do so - there is a specific timing between the lever gears and the bolt assembly that must be kept in order for the action to work properly and you have to make sure that this timing is maintained upon reassembly. The maintenance manual that Browning produced for the earlier BLRs refers to a trail and error method of syncronizing the gear positions until everything is right.
Although the 308 is probably the most popular BLR chambering, I too would vote for the 7mm-08. The 243 is also an excellent choice for range work, but you may want something a little bigger for whitetails and, particularly, for hogs. And I have to say that hunting use is where the BLRs really shine, as they are a real pleasure to carry in the field.