Sounds like you have been bit by "the disease". You have gotten a lot of good advice. You can do it for probaly $1500 to $2000.

I had a custom rifle built by a gunsmith in Georgia. He took an Interarms Mark X and turned it into a .300 H&H. It is now on it's second stock. Dennis Olson of Plains MT recently barrelled it for .375 H&H. This is what it looks like in it's latest incarnation.
[Linked Image]

I would have to say build yours on one of the Mausers. Boyd's or Richard's Microfit has stocks at a reasonable price. One outfit that you might want to consider is the Montana Rifleman. They can supply you a complete barrelled action at a fairly reasonable price. Here are some web sites for you to check out.

http://www.boydboys.com/

http://www.ershawbarrels.com/gunsmith.asp

http://www.montanarifleman.com/

http://www.rifle-stocks.com/

http://www.rimrockstocks.com/

http://www.burnsgunrepair.com/

There comes a time when one must take a position that is neither safe, nor polite, nor popular -- but one must ask, "Is it right?"

Martin Luther King, Jr.