Anthony, Here's a link to a post I made about a stabilizer. If it's still available it's a great unit. I have the older version and it's never let me down. Since you're copying VHS even a older/cheaper unit "might" work. The predecessor to my Sima worked fine for VHS tapes but not on DVD's, although for the price of the Sima I'd get it to be sure, it does it all.
Panasonic combos like the EZ-47/48 would work even with the stabilizer, but I would really suggest the 3576 with a separate VCR for ease. The combo units get kind of complicated when trying to incorporate a filter. It can be done but since the unit only has one display it has to be shared between the VCR and DVDR part. I prefer separate units, or a older unit with 2 displays.http://www.avsforum.com/avs-vb/showt...5#post13625595
If you do with the Panny I'd suggest the EZ-48 over the EZ-47. The whole x7 line('07) IMO is quite problematic. I think they've worked some of the bugs out with the '08 (x8) line.