You have a source for 250 Savage ammo? I haven't seen that on the shelf in a long time. I'd get the gun checked out by a good gunsmith to see if it is sound and then follow their recommendation. If it was me I'd get some brass and handload. You may not be able to find 250 Savage brass but you could get 22-250 brass and size it up.
I've seen current production 250 Savage ammo by Hornady on the shelves of three different stores in the last couple months. I saw Remington and Winchester also at one of the shops with the former was most likely old stock though I didn't check the lot code. The Winchester was in the silver/gray boxes making them a couple years old at least.
Based off my observations of the last couple decades, these latter two companies would do a run of 250 ammo every few years rather than every year as many think. It is not cost effective to make these lower demand rounds every year so, when a run is started, enough to meet predicted demand for the next few years is done after which the machines are set up for something else.
Reloading is really about the only way to go with this cartridge due to the scarcity of loaded ammo. Hornady brass is often available if one wishes to have the proper head stamp. Another advantage of reloading is one can load the 87 gr Speer bullet for use on deer. Based on the results of my 5 examples of 250s of this era, the various 100 gr bullets can range from acceptable to atrocious in the earlier guns as the rifling twist rate is on the slow side for the heavier bullets. I found Remington Core-Loks to be the most likely to give acceptable (often just barely) accuracy with Hornady Interlocks running second.