How fast should I pay off my mortgage?

I know there are some PF blogs out there that promote renting instead of a mortgage, but their primary argument is the cost of maintenance. I'm handy and I think I can offset the cost of maintenance enough to make it worth while. Simply put, I think it's pretty hard to argue against the fact that at LEAST your payments towards principal are something you can recover as capital later on (if you plan to move). Rent is totally lost, you'll never see it again. Also, from what I've heard, you can deduct home depreciation. I have some more learning to do before I'll post about that but it sounds promising.

My current plan is to get a mortgage for around $45,000, putting 15-20K down. According to mortgagecalculator.org with a 15 year mortgage I would have a $412/mo mortgage. That's a lot better than my $730/mo rent now. If I paid $693/mo I'd save nearly $10,000 in interest payments over the life of the loan. Is this worth it? I need to figure out how much ahead I would be if I invested the difference. From what I've read online, considering your home as an investment is not a great idea. But the idea of not having a mortgage payment sounds psychologically inspiring. I'm pretty sure I could pay off a $45,000 mortgage in less than 3 years if I neglect other savings, but is that wisest choice? I could pay the minimum mortgage and invest the difference. Invest at 8% and pay a minimum mortgage at 5%, sounds like I should pay my minimum mortgage... but I'm not sure, I'll have to make a spreadsheet for it.

Anyways, any thoughts on what I should do? Please comment with your ideas!