I wouldn't take a taxi from the BART station. If you're going to take a taxi, I think you'd be much better off taking the taxi from the airport.

As to taxi vs. BART-plus-walk, I'd recommend taxi. Not only is it safer, but it will get you to the hotel faster, especially at that time of day when there's no traffic. And since you're a first-timer in SF, I'd be worried about the (small) risk of getting hurt on the walk to the hotel, since you'll have to figure out your way around. But if the money is a consideration and you're a tough traveler, then you should be okay with the walk.