Experian has a number of useful articles about being an authorized user; this search on their site lists them.
In general, being an authorized user should not require a credit check. You are not truly responsible for the debt; if the debt goes into arrears then only the owner or a co-signer could be sued. Of course, you're married, so this doesn't really help you, but it's explaining how the system works.
Being an authorized user may not help your credit substantially, but it shouldn't hurt. You should be aware that it isn't guaranteed that the particular credit card company reports authorized users; Experian reports that some do and some don't.
They also suggest rather than adding you as an authorized user, adding you as a joint account holder if your wife is willing to do that; that will have a more significant impact on your credit. Of course, there are drawbacks there, particularly that you will be responsible for your wife's decisions with that card - don't ignore this even if you're sure you'll never divorce, as most people are sure at some point. A joint account holder would be liable for the other holder's actions, while an authorized user wouldn't, while she would be liable for your actions in either case.
If they do report authorized users, it seems like which one you're going to add will depend on the weaknesses in your particular credit report. FICO doesn't disclose how they calculate their scores, so you can't know for sure, and they almost certainly do not fully value 'authorized user' status identically to a regular account, so this is hard to answer completely. I would wonder if a larger account would be better than a longer open account in most cases, as long as your utilization isn't great (ie, if one of the 'weaknesses' of your report is too high of a % of credit used); an authorized user clearly has access to the funds in the credit card, and while the 'good payment history' part isn't very telling, the access to funds is.