I picked p a Finnish mosin with no stock on the cheap, I guess around a year ago, 100$. I had intended to find a Finnish stock for it, seeing that there are gazillions of mosin stocks all over the web, I thought it would be an easy venture. I did find a couple, in the 4-600$ range. at that point, noticing the guts of the barrel weren't beautiful either, I decided to just chop it up and have fun. you should get your mosin first, and see if it shoots to your demand, then decide the upgrades your need. or if you just WANT to sport/bubba a mosin, I am all for that too, their are plenty of pristine samples out there for the history books and museums.
if you buy one, and bagged it can't do you better than 3-4", they fix may be simple. I will leave the trigger out of it, although the trigger may make you a better shooter, it does nothing to the actual accuracy of the gun, and with enough practice you would be able to shoot the same with the 100$ upgrade or not, the Timney safety is nice, but not needed. that said, I do have the 3# Timney, and have not regretted it.
1st problem area is the stock. your choice whether you want to put the stock in the closet and buy another, or bed the original. even the couple mosin's I decided to keep "original", I still bedded the stock, and it makes a great improvement, one rifle made a huge difference in accuracy. I also love the aftermarket stocks available, and the Archangel I bought is about as tight as you can get from the factory, it also has a pre-fit inlet if you really wanna go for that saftey'd trigger.
2nd problem is the crown, on the long 91/30's hey are ridiculous, that alone may be a reason to get the 44, they seem to have done a better job after chopping it down. If you get a 91/30 and you want a recrown, it will unfortunately require cutting off about an inch of the barrel, then dealing with sights.
If you should find a decent condition specimen, with a decent chamber/bore/barrel, then do a good bedding job, it'll likely get you to your desired level of accuracy to 200 yards easily, especially with some decent ammo. If you are okay with a scout scope type set-up, the mounts are affordable and not permanent, I would personally want a scope of some type hunting to those ranges, but I am t an expert rifleman, maybe you are fine with irons. I much prefer are standard scope set-up, which required drilling and tapping of the receiver, the base mount is super affordable, but also requires buying a pre-curved bolt section or modifying the original(I modified).
the other option for optics, if required, is the "sniper" type mount, I know little about this, so you will need to investigate the process, but I believe requires no bolt mod(maybe I am wrong).
but like I said, you need to get your rifle and then access the accuracy with a couple types of rounds. I have found in my travels that 44 is generally more accurate without any work that the 91/30, which I assume would solely be the fact tha it has a better crown. when you get your rifle, check out the vids from iraqiveteran8888 on sporterizing your mosin, he does great videos on the bedding and other simple modifications, as well as the deeper stuff.
here's the vid on bedding .note it has like ten parts, as well as installing pillars if so desired.
https://www.youtube.com/watch?v=VFeDm7DMgzo
if you WANT to sporterize for fun, then go for it, I had a great time and didn't spend a great deal of money, I ended up with very interesting, fun and decently accurate rifle. overall I think the whole thing was less than 400$ and lots of time. Mny will tell you to go buy a hunting rifle with optic for 300$, and that's also a great option, although not very much fun.
ATI scope base for receiver(drill and tap + bolt needed)
http://www.amazon.com/ATI-Mosin-Nagant-Scope-Handle/dp/B000O7D2XG
Brass-Stacker "scout" type(very little alteration)
http://www.amazon.com/gp/product/B0..._m=ATVPDKIKX0DER&pf_rd_r=0VCCA0TERWR87G3TQBGM
Triggers are pricey and if not restocking, will require cutting of wood if you want safety, but it is really freaking sweet.
http://www.midwayusa.com/product/559350/timney-trigger-mosin-nagant-1-1-2-to-4-lb-steel-matte
after that, your imagination is the limit. stock choices are endless, with custom woodmade stocks to plastic "tacti-cool" stocks like mine. their is a member here that makes amazing pieces that I hope to purchase in the future. he also sells nice bent custom bolts
http://www.biggorillagunworks.com/
my baby, shoots pretty good. 1 1/2 on good days.