The tools to change the barrel and set up the new one (action wrench, barrel nut wrench, and headspace gauges) are going to cost you around $100 to $150, depending on how you do it. If you only do one barrel – it is probably not worth doing it yourself other than for the satisfaction that you get.
I’ve had OK luck with the Shaw barrels, and you can generally find them for under $250 plus shipping. Be forewarned that you’ll either pay an additional fee to have somebody mark the barrel for chambering or you’ll have a rifle with no visible external markings to tell anyone what it is safe to shoot - Shaw only marks the barrel on the breechface itself and it’s pretty hard to read once everything is put together. Locally, the cheapest I can get the barrel electro/laser engraved is $50, raising the price of the barrel as installed to just under $300.
There are a number of other companies that make prefit Savage barrels, most of them costing between $300 on the bottom end to, say, $900 or more on the top end. I have used Shilen, McGowan, and X – Caliber with equal satisfaction. For my non-critical needs, I have tended to gravitate towards McGowen or X-caliber simply because of the ease with which I can order a barrel online from a very wide variety of chamberings and rifling twist rates. Simply put, they make it easy for me to spend my money and their product is adequate to my needs.
As an aside - Shilen also only marks the pre-fit on the breechface, so a finished rifle using a Shilen barrel will have the same issue as the Shaw; either no visible chambering marks, or the additional expense to have the barrel marked.
There are many higher-end manufacturers that I have not used, because my needs don’t dictate the additional cost and/or manufacturing time. There are others on this forum who have experience with those higher-end barrels, and can provide you feedback if your timelines or budgets allow you to exercise those options.