Howdy TJV,
Tim gave you solid advice above. If everything checks out excellent, you have to decide if you want it as a shooter or a collector piece. If a collector piece then the receiver being drilled and tapped is irreversible and collectors frown on these things.
As a shooter......these rifles have the ability to be quite surprising. The advantage of the receiver being drilled and tapped is you can use a modern scope. However, its possible to get a barrel mounted scope base that works with modern scopes. If you like old barrel mounted scopes, and some are pretty good, these can be had for vintage rifles.
https://www.gunbroker.com/item/844620554
The linked rifle is not mine, and Im not associated with it in any way. If I were right handed Id be tempted by that if I didnt already have some 37s. Collectors wont be swarming on it because of the changes, but they can be reversed if you choose to chase parts......an expensive and aggravating game.
Front sight is not a problem.
Single shot magazine can be had from Steve Earle Products for $95ish and are as good as the originals without entering the collector market to pay for an overpriced single shot adapter.
A better buttplate assembly can be had if you are a position shooter. I have an excellent Anschutz 1413 International Free rifle. One of my 37s outshoots it. I suspect the other will too, have not shot it yet. To be fair, both have older custom barrels, but 37 barrels were usually outstanding. The 37 was made to a high quality standard and it becomes self evident when you handle and shoot one.
Now, for me, this would a be big selling point of this rifle over the one you are looking at. Yes, by the time you buy this rifle and pay shipping youll be a bit more into it......at first. This rifle has a Vaver rear sight if I recall right. Youll have to buy front and rear sights for the one you are looking at. Rear sights are more expensive than front sights. So really, you are already ahead with this rifle.
Now, THE BIG thing about this rifle is that it has a Canjar trigger. Those are hard to find and expensive when you do find them. Ive seen some in the $400-600 range in the last few years. Youll like the Canjar trigger far better than the factory trigger. All things being the same condition wise, the trigger would sell the rifle to me. That custom stock, Dunlap or another that escapes me right now, should prove comfortable. The palm rest can be sold to offset the cost of the rifle if you so choose.
Whichever way you go with it, I think youll be impressed with the rifle. Shoot a wide variety of match ammo in it and you just might surprise folks with an old Remington 37.
Take care,
Greg