We have 50 years of petroleum left and maybe 100-200 of coal. Compare that to centuries of Uranium, Plutonium and other radioactive minerals. Also, emissions are a big deal, too. Nuclear waste is contained and far less dangerous (when kept properly) than fossile fuel emissions.
I'm a long way from an opponent of nuclear power, but when you say
Nuclear waste is contained and far less dangerous (when kept properly) than fossile fuel emissions.
I think you might be making the opposite point to what you intend.
You compare the worst case of safety & long term consequences for oil/coal (ie, the current situation), with the best case ("when kept properly") for nuclear power.
A better comparison would be to compare the safety coal/oil power after spending the money required to keep nuclear waste safe on cleaning coal/oil emissions and improving mining safety, or else to compare the worst case in each scenario.
The worst case for coal/oil is a few thousand dead (from mining) a year, and bad climate damage. The worst case for nuclear is a few million dead and regional environmental catastrophe. It's fair to have a discussion about the probability any disaster happening, but to preclude the possibility undermines your argument.
To me, nuclear proponents making the case the nuclear is safe if everything goes well sound a lot like the NASA administrators who Feynman criticized in the challenger disaster report for not understanding risk.
Sure. Major investment and infrastructure improvements are needed to make its alternatives viable too.
EDIT: I should note that even the above is somewhat irrelevant to my original point, which was simply that one cannot dismiss nuclear power as a whole simply because one type of fuel supply is "limited".
No, they aren't. And the only reason nuclear is considered "cheap" is that the costs of accidents and waste disposal are methodically underestimated.
Oh, and another thing: Uranium fuel is a quite limited resource as well...