Also note that 1 gig of ram is not a lot anymore. we run so much crap now like anti-virus, web programs, or any other background services running consider turning some off. ChkDsk and defrag is never a bad idea and try to keep decent HDD free space (20% +). All have been problems for me on an older machine i had.
I am not saying you cannot run the game without buying new hardware, but i run everything on max settings and ive only lagged once during a modded - very very large battle. with all the math going on i would point my finger at the Ram before the video card because its really not THAT demanding from what ive seen, tho you can get a decent upgrade for less than 100 bucks... and i would if you can

and your cpu is fine. Now if it was only massive battles doing it id say video card, but your saying game progress meaning more memory keeping track of all the progress.
figure out which you can do easier - new PCIe video vs goin up to 2 gigs ram. either would help in my opinion.
Good luck