I don't see how this topic could avoid at least touching on politics, since we are talking about core issues that could change the face of our economy, our environment, and our very way of life. At the same time, we have to remember that beyond politics there is the reality of the situation, and that if we can offer ideas and suggestions outside of politics, maybe we'll come up with some useful approaches that will actually make a difference.
Drilling ANWR would help keep oil prices lower. Any new source of oil would do that. At the same time, I think that it is important to understand how much of a difference ANWR could make; current estimates place the size of the reserves in ANWR as equal to US consumption for 1 or 2 years. Obviously the US wouldn't get all of its oil from a single source until it was tapped dry; but say that we pumped 1 million barrels per day (about 5% of US consumption) from this reserve; the reserve would last perhaps 20-40 years, but only make a very small change in oil prices or energy independence. IMHO ANWR would make about as much difference as getting people to carpool for 1 commute per week (but I've not really done the numbers in details, and am willing to be convinced otherwise.)
We could do something like build enough drilling and pumping capacity so that the US _could_ get all of it oil domestically; but then elect to keep that capacity in reserve, buying oil from the cheapest sources, but if needed we could turn the switch and basically boycott external sources. That might get them to keep their prices lower...but all of the necessary unused capacity would essentially amount to a tremendous tax.
Nuclear power is another approach, on that is both potentially much cleaner but also much scarier than continuing to burn oil.
The problem with nuclear power is the waste issue; the discussion of waste gets focused on things such 'how do we bury the stuff for thousands of years', but the _real_ way to deal with nuclear waste is 'nuclear incineration' or 'actinide burning'. Basically this involves processing the used fuel, and separating out the various radioactive species to be dealt with in an individually appropriate fashion. (The really violently radioactive stuff is just stored; it is gone after only a few months; the stuff that lasts millions of years isn't particularly dangerous so you bury it, and everything in between you run through the reactor again to convert into one of the two extremes.) The problem with this is that you have to use exactly the same isotope separation technology that you need to build a bomb; so using nuclear power becomes a problem of _people_; do you trust other people with access to the technology to build atomic bombs.
Biofuels are an attractive possibility, but right now we still don't know how to do them. Corn ethanol has been a disaster; a political sop to big agribusiness with lots of green paint; the problem is that it is not energy positive as currently done. Soy biodiesel is at least energy positive by a significant amount, but we don't have the available cropland.
I could babble on and on
-Jon