I just got out of all my Savage rifles but one and I will say they are a great way to cut your teeth in all this long range stuff but once I really wanted to start getting consistant past 700 yards I sold em and went custom. As far as which ones to stay away from I think that's a little up to you and what you want out of them. I had an older flat back 116 and it was pretty nice but I dumped a ton of money into it new trigger, trued, bot handle, lift kit, recoil lug, and a machined barrel nut. I also had a .243 with an action from a newer accu-trigger that I did almost nothing to and it shot great. Overall if your going to buy an out of the box gun and leave it at that I would get any of the newer 116's or any of the specialty models. If you want to tinker then find an older 3 screw flat back and go for it sky's the limit. There are also a ton of aftermarket stuff to do your self I've purchased several Stockade money saver stocks and a couple different barrels to play around with. I had a ton of fun messing around with Savages but at one point I just got sick of tinkering and wanted a great consistent shooter but the self taught knowledge you'll come away with at the end of your Savage journey will be priceless.
The only savage I regret buying is maybe my Bmag, and that's because its not twisted enough for 25's. Other than that even my Savage Axis 22-250 heavy barrel shoots sub moa after some trigger work. My 10 .243 benchrest accurate.
Depends on what your plan is?
Buy the cheapest one you can find because they are money pits!
Years of dealing with Savages have shaken out that I don't likem for hunting guns but work well for high population varmint guns.
Most of my experience is with the later model, heavier barreled Savages with the Accutrigger. I own a 6.5x284 LRH, 260 LRP, and 22-250 Predator. Interestingly, these rifles as well as a couple of 22 rimfires were won(some raffles, some for score) at competitive shoots over the last several years Savage was sponsoring shoots on a regular basis here in the Northeast. Generally, most of my rifles are custom/semi custom. When I got the first one, the LRH, I didn't have very high expectations but was pleasantly surprised. With the exception of a little sanding of the barrel channel to free float the LRH and Predator, I haven't made any modifcations. With 400-800 rounds through each of them, they all have been consistent performers with excellent accuracy. The LRH and LRP are capable of .25 MOA out at 500 yards. I have several shooting buddies that have had similar experiences. At least with the heavy barrel models, I don't think it is so much a question of which one not to buy. I think it's more about acquiring a representative example. While it seems rare with the Savages, we have seen some examples that didn't shoot well. This is the bane of the factory rifle.IMO.