You should adapt the drain to 1-1/4. That is the standard size for a lavatory basin. These fittings are readily available at any plumbing supply store, it's call of all things, a trap adapter! You can easily recognize it, it has threads on one end and there is normally a white cap screwed to that. P traps are also easily found in the plumbing supply house. The usually come in a package, like a kit, that has all of the components you will need. Sales people usually can answer questions about traps without getting into too much trouble. After the adapter is solvent glued to the drain, everything else is hand tightened slip joints. The only place you can go wrong is with the cone shaped and thin flat washers.