They have four types of subscription packages:
yearly Web Pack (19¢/day)
monthly Web Pack (26¢/day)
yearly+dialup (27¢/day)
monthly+dialup (52¢/day)
The dialup packs (you do not have to use the dialup service) give you subaccounts so a whole family can have premium. The web pack is for one person, and you get one alias with that. Slots open up occasionally at premium.neopets.com, or you can get a referral from another player.
There is no way for someone to get your personal info if they break into your premium account now, since that information was removed. Plus the actual service is not Neopets, it is with a company called
VSI.
One great benefit of Premium: since they can verify who you are when you contact them, if your account has been broken into they can return it to you within the day. There is also a Premium only frozen form, so you can possibly clear up a misunderstanding much faster and get back to playing. (If you've been naughty, though, you'll be iced for good...they don't play favorites with Premiums!)
Add to that the complete removal of ads, Super Shop Wiz, portal modules galore to organize your play and give you alerts, and Premium portal and Neopets report/bug forms, and you're all set to be one happy player
It's not for everyone, it rather depends on your playing style. It suits me to glance at my portal and check on my stocks, guild, plushie tycoon, multiplayer games, etc. all at once. SSW is nice, since I stink at RSing and don't care to refresh the SW over and over and over, but those same prices do appear on the SW.