There are many ways to do M/T work, but I prefer using a router and jig with either fixed or floating tenons. The Leigh FMT is a great jig that is extremely accurate and does a great job, but it's expensive. While I have one, and love it, it's not really a total solution and definately not the cheapest solution. Other jigs like the Pat Warner jig can be made or purchased to make the mortises for floating tenon joinery. Then you make tenon stock with a router table and table saw to fit the mortises that you made. If you are on a tight budget, this method is preferred, as you can even build your own jig if you are on a tight budget.
Chairs with round spindle legs are usually assembled with round tenons that are inserted into mortises that are drilled, usually using a forstner bit, into the mating part. Square legged chairs and tables tend to use more traditional rectangular M/T joinery. You need to investigate your design and determine your needs, and budget, before deciding what you will need.