Yeah, many people have done this over the years. The ATI synthetic stock isn't bad, and I've played with a few sporterized mosins.
Some of the drawbacks - scope mounts REALLY inhibit loading the mosin. Stripper clips, are now a thing of the past. Not a big deal, if you're just dear hunting, you shouldn't need more than 5 shots in a weekend, right? They kick like a son of a gun when they've been put into a nice light stock to hunt with, so watch that scope bite! My buddy and I were both high-fiving each other's foreheads, for the rest of the day. For what you're looking to spend, you could actually get a used remington 700, in something that's not 7.62x54r... Which, isn't a bad cartridge, but there's only about 3 guns in the world chambered for it.
I had a mosin for a while, and it was alot of fun to shoot. Very accurate, as well, with the iron sights. Couple things I would do to it, should I get one again (I probably will, they were alot of fun), I would change the stock for sure, but those boyd's stocks are expensive! Either the ATI stock, or modify the existing stock. I'd remove the majority of the forend, the heat shield, and add a pistol grip and cheek weld. There's a scope mount for the mosin, that mounts the scope FORWARD of the ejection port, so you can mount a long eye-relief pistol scope. 4-6 power is awesome. I saw a guy who had used some wire and drilled the back side of his bolt, then installed a finger-loop, so that he could easily work the safety with 1 finger. Lastly, tune the trigger and sear to a nice pull. Mine had alot of take-up, a real crisp break, and not alot of over-travel. I've seen some just be real long and gritty, with tons of over-travel. I'd work all the excess out.
Some of those mosins can be worth some stupid money, so do a little digging around and make sure what you have is indeed a $99 big-5 special, before you go chopping it up, just to be safe. http://7.62x54r.net/
has alot of good historical info, but it's a purist site, so you wont find alot of sporter info there.