Regular soap will shorten the life of your leather. Saddle soap is specifically formulated for leather and contains no free alkali that will damage it. Saddle soap is available at tack stores, where shoes are sold, and you should be able to find Kiwi brand saddle soap at any Walmart or CVS.
Glycerin saddle soap is a step up because it will moisturize the leather a bit while cleaning.
Feibings makes great products and has soaps and conditioner on their site:
When cleaning, soap in sections and then remove the soap immediately with a damp cloth. Try to use as little water as possible. When finished dry them with a clean cloth and then set them rolled but unbuckled to air dry.
If they get particularly sweaty after play, give the inside a once over with a damp cloth to keep the salt from sitting.
On conditioner- unless they are going to be exposed to the kind of conditions that saddles or boots suffer (sun, wind, rain, etc) they shouldn't need conditioning for quite awhile. Glycerin soap alone will keep them nice and soft. There is also always the possibility that conditioner will darken white leather. If you decide to condition, you can test this by putting a small amount on an inconspicuous area of the cuff and let it soak in overnight. If you decide to proceed, spread a thin layer over the cuffs and let it soak in. Wipe off any excess the next day with a clean cloth.
Avoid conditioners like mink oil (animal cruelty, has silicone, can go rancid), neats foot oil (synthetic), and Lexol (known to cause allergic reactions). I would recommend Aussie (available on the Feibings site) or Chelsea Leather Food.