You can just pick up a Hoppes kit which should come with oil. It will have everything you need to get started. After a while you will probably want to pick up an extra brush, Q-tips, and an extra bag of patches.
Yes a cleaning kit for your particular caliber is one of the first "extras" you should buy. While you're at the sporting goods store/gun dealer, pick up a few extra BRASS brushes for your caliber pistol (I feel the stainless ones are too harsh on the bore). And as Curlyjive mentioned... Break Free is a solution a lot of people use for cleaning their guns. On the way home stop by the grocery store and get a large packet of cue tips too. Applying a drop or two of your cleaning or lubrication compound to the tip and using that in the nooks and crannys of the gun (especially the slide rails) will prove to be a handy solution to an otherwise more difficult problem. Old toothbrushes (or new ones if your dentist includes one with you tooth cleaning sessions... thanks Doc!) also come in very handy. Be sure to wear a shop apron or have an old towel handy so you don't besmirch your tux when cleaning your gun. (Formal wear not recommended when gun handling unless you're James Bond or something!).
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