Welcome to Washington...here are a few things:
* You don't have to be worried with safety on the Metro at all, you'll be fine - especially in Virginia.
* You'll be fine in Crystal City/Pentagon City at any point in time, if it's 3 a.m. on a Sunday or whatever.
Now on to the options:
* I don't blame you if you don't want to do it, but firstly i'll suggest walking to the hotel, depending on what hotel you are in. The airport connects directly to the Mt. Vernon Trail and then onto the 'Water Park' in Crystal City (on Crystal Drive). From there, walking to any of the hotels is as easy as looking at the map. But, you said you had a bag, are female and obviously are concerned about security, so this option probably isn't your best option - since you aren't familiar with the area. Just to make it clear, if I got in at any point in time, I'd easily walk home (my place is between Crystal City and Pentagon City) with a few bags - instead of taking the train or a taxi.
* Metro isn't a bad option (at least you aren't stuck with the ridiculous fare schedule coming in on the weekend), but as others said - you'll probably have to wait for a few minutes to catch the train. One stop North and you'll be in Crystal City. Once you get here, depending on which hotel you are in, they'll be a walk 'underground', which is always (24 hours, even on weekend) staffed with security and has a bunch of cameras [there are a lot of DoD facilities in here which need security]. Also, there is an above-ground exit to Crystal City where you can walk to your hotel on the streets. As others have said - you'll be the only one on the streets for sure, it will be a ghost town for sure probably from about 21h00 on to about 10h00 Sunday Morning in Crystal City, but you'll be safe, for sure.
* A taxi is an okay option and obviously the easiest since you don't have to lug bags - but the meter will probably run about US$7-10 for the few blocks to any of the hotels nearby, plus a tip.
Enjoy your time here!
-jeremy