You can buy an inexpensive scope for that gun but then you run a huge risk of scope failure when you are miles/days and $$$$ into your hunt. Is that really what you want to do? Buy either a Leupold or an Alpen scope designed and rated for BP. Spend $350 and on a reliable piece of equipment. That's my advice.
I use an older model Leupold Vari-X II in 3x9 with an adjustable objective. This was my first Leupold and now I own several that I use on target rifles, .22’s, etc. You cannot go wrong with a Leupold. They are super bright, have lots of eye relief, are very rugged and hold their zero when changing power settings.
I used the 3x9 AO on a Thompson Center Hawken .50 (with a clamp on mount), a .50 Ruger 77 Muzzleloader, a Remington 700 BDL in 30-06 and a Marlin 336 in .35 Remington. If you lap your rings, you can move a scope from rifle to rifle without bending the tube.
Whatever scope you purchase, be sure that it has a low power setting as this is all you need with a muzzle loader, even out past 100 yards. At higher power settings, the field of view is greatly reduced. When hunting, I would use the 3X setting. On the range, I would zero at 9X and then turn to 3X for a confirming zero. If your Savage is the smokeless powder version, you may hunt at longer ranges but, even with a 30-06, I still used the 3X setting.
I hunt the Kentucky woods where the typical shot is about 50 yards. I did take one nice 8 pointer at about 135 yards. I shot a nice 10 pointer on a dead run at about 75 yards, a massive 10 pointer at about 25 yards and probably over 50 other deer from 1979 to a few years ago.
The older Leupold Var1-X II is super bright and the Adjustable Objective feature lets you select the best setting for minimum parallax at whatever range you are hunting.
Newer model Leupold’s are even better. Going back to just after WW II, Leupold has never made a bad scope. I think that the Leopold engineers were involved in making optical bomb sights and learned to use nitrogen filled optics to prevent fogging at subzero temperatures.
Don’t buy an inferior scope as you will be disappointed. IMO, once you have used the Adjustable Objective (AO) feature, you will want it on all your scopes.
I would watch Ebay for a buy on an older model Vari-X II scope. You should be able to find one in the $250 - $300 range.
I have a Leupold #65475 Ultimate Slam 2-7 X 33 with the S.A.B.R. reticle. I think I got it on special for $200 from Optics Planet. Its close to your price range and made for BP rifles. I have it on my Austin-Halleck 50 cal. Highly recommend it.
I have the Leupold UltimateSlam in 3-9x 40mm on my T/C Omega. I've never found 3x to be too much magnification, the larger objective lens allow more light transmission and it's really nice to have 9x for testing load recipes as it helps determine if a poor shot placement was due to operator error or a load the gun just doesn't like. The parallax is set where it should be for shotguns and muzzleloaders - 75 yards - where most other "regular" riflescopes are set at 150 yards.
I've used various scopes on the Savage ML. Depending upon how far up the scale you want to take the velocity, the recoil can get pretty stiff, easily in the 338mag rifle class. Given that, I would advise against any cheap light duty optics. Stay with mid level Leupold, Nikon or similar quality scopes and you'll be fine. I've had a 2.5-8x VX3 Leupold on mine the past few years and it works very well for my hunting.
I have a Leupold VX-1 2-7x33 on 110ML stainless. Bought the scope in 2012 for $210 from Precision Scopes and Optics and have been satisfied with gun and scope. Leupold has a life time warranty and really $210 for a decent scope is a deal as far as I am concerned. Do not go cheap on optics, quality is long remembered after the price!
The recoil on my Savage is no where as much as my 338 Mag. I have shot deer at 240 yds. and need a little more than 2 x 7X. A decent quailty scope of about any manuf. will work well. Low power if shooting in tne woods or brush, higher if you hunt open spaces like I do.
Don't know what you are loading in your Savage, but if you're staying close to the "book" loads the recoil isn't much to be concerned with. I have several loads I occasionally hunt with that give a 300gr bullet 2350-2400fps, 250s considerably more and the recoil they generate will easily match my 338 and approach my 300 RUM.