Verbatim's Crystal top coating has always shown fingerprints. I don't find them any worse at showing fingerprints than any other silver-topped CD-R (maybe even slightly better). But they are a bit more difficult to remove. Try a good quality microfiber cloth, and maybe moisten the disc surface slightly by breathing on it.
I love them though. Best non-printable disc surface ever! The surface is a bit like some inkjet photo paper and seems to absorb the ink, which makes it much easier to write on with a fine marker pen and smudge resistant. It also offers superb protection (I've seen far too many unbranded TY with the reflective layer flaking off or with pin holes).
The surface shouldn't feel greasy though. It will feel different to other plain silver CD-R (a bit like some porous ceramic inkjet papers), but if you think it is greasy on a new disc which hasn't been handled then I urge you to contact Verbatim Europe. (Maybe there is a manufacturing fault and the coating hasn't set properly?)
As for long-term data storage: Verbatim DataLife Plus / AZO CD-R (mostly Made in India by Moser Baer) have been my standard choice for over a decade and I have had no degradation issues at all. But I don't buy them any more. Since 2009 I have had too many problems with the quality - in particular visible dust spots in the dye layer (which result in clusters of E22 when scanned). So far this hasn't affected their longevity and I may try them again. The quality of Moser Baer made Verbatim DVD+R has improved in the last couple of years. And so has Verbatim Europe's customer service - earlier this year they actually replied to an e-mail. (For the first time in 5 years!)