An Uni-T UT61E costs less than 60$ and comes with pc connection cable (serial connector or usb)... the one with serial cable you can simply use a serial to usb cable to connect it to pc.
The meter is supported by UltraDMM which can log several multimeters at the same time.
The only problem I can think of is that the UT61E updates just two times a second, which may be a bit slow for you. It drops update speed in favor of lots of counts (22000) and precision.
There are other meters supported by UltraDMM , including UT60A, UT60D, UT61 A/B/C/D/E etc
See what's cheaper on eBay, see reviews, see whats more convenient and which one gives you the best deal.
Ah almost forgot, there's also this Digitek meter sold by a guy that's a user on this forum and has a very good reputation:
http://www.ebay.com/itm/Digitek-DT-4000ZC-TekPower-TP4000ZC-Data-Logging-Multimeter-with-Temperature-/200912705694?pt=LH_DefaultDomain_0&var=&hash=item2ec754989eIt also has logging, it's not supported by UltraDMM but has the software to log stuff with it. It's cheaper (<40$ with shipping). The only "problem" with this meter is that it uses the same jack for current and voltage, so you have to be careful and select what mode you want the meter to be in BEFORE you plug (or connect) the cables.