The cheapest and easiest route is to rebuild the one you have, it's not that hard really and it costs next to nothing.

The stock carb is designated a 40mm though the inside of the throat narrows a good bit.
From a $$ standpoint, I have to agree that rebuilding the old one with a new set of jets, needle, and gaskets would probably be less expensive...assuming the slide with the rubber diaphram is in good condition and without any air leaks.
If you want a new carb then the least expensive carb you can get is a Mikuni VM roundslide carb.    The 36mm size is the size you would want for a stock engine.  A modified engine with larger piston, more compression, perf carb, perf cam, etc,  could use a 38mm or even perhaps 40mm size, but the 36mm can handle anything a Savage engine can throw at it...even a highly modified one.  
The larger the carb bore the slower the air velocity in the carb throat, and the slower the air the less responsiveness/power and smooth running  you get in the low to midrange.  A large carb bore will benefit max power at max throttle.  But since we spend most of our riding in the low-midrange then that is where we want to maximize the power & torque.

Anyway, the Mikuni VM roundslide 36mm is the best bang for the buck I have found, that is why I use it in the carb kits.  At a bare minimum you need the carb with some extra jets for tuning, a new rubber mounting flange (different size from the stock unit) and a new throttle cable to match the carb to the Savage hand throttle.

You will not find any replacement carburetor I am aware of that you can just slip in place of the stock carb due to the mounting and cable hookup issues.
Keep in mind that the VM carb is not just a performance carb, in fact it would better be termed an efficient carb.  A stock carb is designed with restrictions for the purpose of minimizing exhaust emmisions.  The VM is just a good basic carb that will allow the engine to breathe in a normal fashion, and the result is more power, torque and responsiveness, especially when combined with a better flowing muffler...there again allowing the engine to breathe normally without restrictions.

I can put together a bare bones setup or if you want to do it yourself I can give you some of the info you would need to get the correct flange and cable you need to go with the carb.

One other option is if you can find an inexpensive 38mm Edelbrock Quicksilver on ebay, they will fit the stock mounting flange fairly well but will still need a new throttle cable.  Also, it will be necessary to purchase additional needles so it can be tuned to match the Savage.
These are good carbs and work very well on the Savage when properly tuned.  In the past they were easy to find on ebay for cheap but that is not the case now days, the price is usually well over $100 BUT if you are patient you can on occasion find one for less.  I found one a couple of months back for $50; it needed A LOT OF CLEANING but is in decent condition with some slight wear on the slide.  A lot of dirt/grit will grind down the aluminum quickly.

Ruminate a bit on the info, and others will add their perspective as well.  Let us know what you decide.