I have stock several rifles and have never used a router. Unless you have a way to completely control and guide it when doing your cuts, it is very probably it is going to jump on you and screw up your work. I really doubt a router is going to save you much time or work. Rather than buying power tools, buy high quality hand tools.
You can square the stock, top and one side with a hand plane. If you know someone with a jointer, use that for the top surface and one side. A planer isn't going to really help you out because you must have the top 90 degrees to a side and planners only make the side parallel.
Start by laying out a center line down the top of your stock. Using your action, figure out where to drill through the stock for the guide pins/rods. Basically these are threaded bolts with the heads cut off that screw in action to replace the screws that hold the action into the stock. They act as a guide when you are inletting your action so it is always in the same place when you are checking the fit of the action into the stock.
You can use your existing stocks to get an idea of how much wood to remove. You are going to need inletting black that you can brush on the action and barrel to see where to remove wood. It is kind of slow but you will quickly figure it out and with sharp chisels it is easy to do.
For the barrel channel you can start with a half round chise; to get the channel started and centered. Then go to a barrel bedding tool of the appropriate diameter. Brownell's offer these: http://www.brownells.com/gunsmith-tools-supplies/stock-work-finishing/stock-making-hand-tools/barrel-channel-cutting-tools/barrel-bedding-tool-prod6796.aspx You can probably use this to get a barrel channel as fast as a router when you consider the set up time for a router.
Once you get your action inletted then you can set up your outer stock dimensions. Everything on a rifle stock is based on where the trigger is, the length of pull and drop of the stock and the length of the forend. Shaping rifle stock first then trying to get the action in exactly the right place is really difficult. Since you have to inlet the action and shape the stock, do the inletting first.
Really recommend you get a cabinet makers pattern rasp like this: http://www.brownells.com/gunsmith-tools-supplies/stock-work-finishing/stock-making-hand-tools/patternmakers-cabinet-rasps/patternmakers-cabinet-rasps-prod5188.aspx I have used the same one for 35 years on numerous stocks and other wood projects, so though expensive they are more of an investment in a good tool. They remove wood quickly, are easy to control and make stock shaping go quickly.
Over all go slow because you can't replace wood you remove. While you can cover up inletting mistakes with bedding compound, you can't do that on the exterior of the stock. Good luck on your projects. There is a lot of satisfaction in doing your own work.