I'm trying to build myself a long distance rifle but don't know where to go from here.
Well, people typically do some research into what is currently in use and successful and then proceed from there. First of all, can you describe what you mean by long-distance rifle? If you mean a rifle for shooting 1,000 yds+, then that is generally referred to as a long-range rifle. If 1,000 yds is not in the plans, then you can build a target rifle for shooting to 600-800 yds.
have decided on starting with a classic Mauser action in 6.5x55 Swedish.
Not the best action for a long range rifle. Most serious builds are done on a Remington, Savage, or aftermarket action like a Surgeon or a Panda or BAT. But you can use whatever you want, just realize going into it that there are minimal parts available for Mauser actions, and there will be many other challenges in the quest for accuracy.
Your choice of cartridges is not bad, 6.5X55mm Swedish is a very capable cartridge, and there are .264" target bullets available. But, again, there are better choices.
For the barrel I want to have between and 26" and 28" for a full burn with a 1:8.5" or 1:9" twist.
A 6.5X55mm would be at peak efficiency out of a 26" barrel, I don't know if you would gain much with the additional 2". You understand that 28" is a special order barrel, right? Most barrel blanks are 25"-27", but you can have a barrel made any length you want up to about 36".
In order to stabilize the 139 gr-140 gr bullets, a 1:9 should be sufficient, but you can order whatever twist you want from some makers (cut rifling in odd twists is easy to do, button rifling is different).
I don't know any manufacturers for where to find a barrel to these specifications and I don't know how heavy I should go.
There are numerous barrel manufacturers, and most have web sites. Study up and decide what you want, most will not advise you. They make barrels for a living, and are good at what they do. machinists turn down and profile barrels, and they are good at what they do. Some barrel makers offer profiled barrels, but they charge extra for it.
I also I know it isn't very powerful but would a muzzle-break be overkill?
I have seen muzzle braks on 22-caliber centerfires, it is a matter of choice. I will tell you, though, that many target shooters do not like to shoot around shooters whose rifles have them (nothing like dropping out of the X-ring to really tick somebody off), and some ROs will move shooters with brakes on their rifles to the far end of the range.
Next step is finding a stock. Any ideas where to start there?
Again, there are several companies that make pre-carved unfinished stocks. You will need a stockmaker to get one fitted and finished in a way that will help you be competitive. That is what I do, I am a stockmaker. There are others in the country, not too many any more I suppose, but still some are out there.
Again, sit down and plan it out first, then find and buy the components, then find a good gunsmith to help assemble the barreled action, then stock the rifle. If you do it right, you will be in action next year.
Or you could just go and buy a good factory rifle to start with and build your dream rifle for next year.
