Dear Guys,
Thanks for all of the spectacular responses. They were exactly what I needed. After reading them all, and going to a gunshop, and also going to a gunshow this weekend, here is where I am.
1. I think that both the Savage 99 and the Win. 88 are both going to be harsh kickers with plastic or steel buttplates. Therefore, no matter what I choose, I am getting the best recoil pad that money can buy and having it installed.
2. I handled a pre-64 Model 88, and it is a beautiful rifle. Also, it was very nicely balanced. But, I have this personal "thing." I can't stand the feel of a rifle that has a square bottom forestock (such as the Ruger M-77). When I hold a rifle like this, I feel like I've got an elementary school chair in my hand, and I keep shifting the rifle different ways to make it feel better in my hand. I can never seem to just settle down with it. This is probably not an issue to people with big hands. I love the feel of a round forestock, with checkering on each side. As beautiful as the Model 88 is, it does have somewhat of a square bottomed forestock, and because of my personal quirk, I think it would drive me crazy. ( I get that same bad feeling when I hold a Remington 760 pump.)
3. It is interesting that several people have told me that they think the Model 88 is prone to breaking down. However, I reviewed the entire 24 pages of the Gunsmithing messages from last year. Guess what. Not a single one regarded a Model 88 malfunction, and probably 8 or 10 regarded malfunctions in the Savage 99s. Of course, this isn't a scientific analysis, but it makes me think the Model 88 is pretty reliable. I also think that the true break-down culpret is the semi-auto Model 100 Winchester, and that somehow, the bad reputation of the semi has spilled over on the lever action.
4. I went and handled several Browning BLRs. My research indicates that these are extremely good and very reliable rifles. They almost have a cult following. But, they are so thin and slab-sided, and so tall in their design, that when I am holding one, I feel like I am holding a pine one-by-six trim board. Again, I know that this is purely a personal thing, and that the modern BLR is probably a better built rifle than the 99 or 88. It probably relates to the length of my arms, the size of my hands etc.
5. I have found through this process that I really like a straight-grip stock on a lever action. It helps to make it much quicker and comfortable in my hands. Since I want a .308, and I don't like the feel of the BLR, this pushes me by default to the Savage 99.
6. I handled several 99s, and there are so many styles and models that the way they feel depends totally on the particular model you are holding. I found a beautiful Savage 99G pre-war, that seemed to leap to my hands. It was in great condition, with original steel buttplate and original untapped receiver, and in 300 Savage. Although the 300 Savage round would probably be fine for me, I know that my rifle must have a recoil pad and that it must have a scope. So, I couldn't bring myself to buy that rifle, knowing that I would end up cutting the stock and drilling/tapping the receiver. It would have ruined the collector value of a fine rifle. (The guy was asking $650 for it.)
7. I hate to give up on the model 88, but I think that at this point, I am steering towards a post war Savage 99A, with straight grip and schnabel forearm, in .308. I think that they weigh just at 7 pounds, which is a half pound lighter than most of the 99s. I know that it will kick, but I think that a real expensive recoil pad, and maybe adding just a little extra weight in the forearm, will help. (If anyone disagrees, please let me know!)
8. Can someone answer a 99 question for me please? Does the post war 99A have a real walnut stock, and does it come with zero checkering, or maybe cut checkering? I can't stand hardwood stocks or impressed checkering.
9. In my original post, I said that many of the Savage 99s felt heavy. One gentleman responded that he never considered them heavy at all, but that he weighed over 200 pounds and had long arms. As many shooters will tell you, the world is a much different place when you are 5 foot eight and only weigh 145 pounds! [Sure that trim 30 inch waiste gets you more dates, . . . . but rife recoil can be murder.

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Thanks to everyone,
Big Paulie