Interesting proposal. I like a person who has a dream and is looking for ways to implement it.
I've scanned the responses and thought I'd add some of my own.
You're right. Most of the "freebie" papers are very liberal in nature. Politically, I'm to the left of most folks here at FR, but to the right of the general public. When I pick up most of the "freebies" I'm often shocked by what I read. One paper in my area is devoted to gay issues, another centers on the performing arts but has Dr. Ruth type column that would shock a sailer. And let's face it, most performing arts and artists are far to the left. But you're right. They are loaded with ads. But look at the ads they carry. The paper I referred to carry's ads for the local "head shop" (I wonder what those rolling papers are really used for), lots of 900 numbers for dating (straight and gay) and tons of "Booby Bar" ads. Is that the type of advertising you want supporting your conservative paper? But then again, who else would you get? Those places seem to make money and have money to advertise.
Second, who are you going to get to write for your paper? I don't care what the people say here on FR, copyright is copyright. And people like Coulter, Will, and others are under contract by their syndicates. Print their stuff and you'll have a law suit faster than you can say Washington Post/LA Times. Same goes for copy from the major news and wire services. And yes, even the lib papers pay to print the Onion. So that leaves you with the also rans (and some of them are great writers who just haven't received the right promotion.) Yet at some point in time, they too will want $$$. You'll have to have someone, if not yourself solicit for advertising, do payroll, pay for distribution and distribution racks, compose and print.
It may be a wonderful labor of love that may blossom.
Regarding the internet, I think the same would hold true. I've seen numerous sights linked to from this site that are similar to what you are proposing. Many have languished. Why did FR, Drudge and Lucianne prosper? They served a niche when a niche was needed. Right place, right time right set of circumstances.
When there is no niche needed, it's very difficult. The others languish because that special niche hasn't been called for and they are also rans of FR, Drudge etal. There are probably 20 other conservative news forums, yet FR is tops. There are several News link websites, yet Drudge is tops.
Best of luck. If you have a dream, don't let anyone get in the way. Even if it fails, it will be a learning experience.