if your just above minimum spec then all you can use is just minimum settings... sorta makes basic sense that 1.
start the game at absolute minimum if its smooth, first increase the screen size to native monitor size... if its still smooth you can then increase things like texture quality first... going to medium first and if again its smooth you can start adding the higher end stuff like soft shadows. as a general rule for all games, things like soft shadows high shaders, smoke and soft smoke, hbao and ssao are all high end and will be beyond your cards ability to handle them smoothly...
1 good thing is the e6600 is a great overclocker and if you have good quality matched ram then theres no reason why you cant get that cpu to 3.3ghz as long as you have good cooling.
you should be able to get away with putting a gtx 560ti in without bottnecks on some games that only use 2 threads. but a more realistic ballanced system would be to max it out at 460 and you would be able to have high settings on some games..
as you have a core 2 duo motherboard you could jump to the core 2 quad with little more than a bios update... so you may get out of the entry level with a bit of spending when you can afford it.