Assuming you're buying a 66cc/80cc two-stroke engine, everything but the bike is included in the kit and you shouldn't need (in theory) to buy anything. Although, you might want to buy some things to replace them that comes with the kit :
-Spark plugs (NGK BP5HS or NGK BP6HS is good), the ones that come with the kit are really cheap.
-New gas lines, the ones that come with the kits tend to become hard and thus fragile.
-New fuel filter, why not?
-New #415 chain, just in case you happen to break it (these damn 415 chains are hard to come by in stores, you're probably going to buy online)
-While you're at it, a chain breaker (good tool that allows you to had master-link-less chains)
-Different rear sproket, your kit will come with a 40 tooth or 44 tooth in most cases. Going down on tooth will give you more top speed at the expense of acceleration, the other way around is true too.
-Metric bolts 6mm, 8mm, 10mm, just in case your engine would break it's mounts loose or something, just buy them, you'll end up using those.
-Head gaskets, they're cheap and it would be sad having to wait for the mail.
I can't really think of anything else really. All those are not necessary but eventually, if you learn to love these engines you'll get them. Also, maybe it's time to change your brakes on the bike.