If you want to take it all the way back to the way Grandma did it, you need cardboard for templates, a pencil to draw them and to trace the shapes onto fabric, scissors to cut the templates out and scissors to cut the fabric. Then you will need thread and needles to sew the fabrics together. You can use empty cereal boxes -- cost -0-; a #2 pencil -- cost less than 25 cents; paper scissors -- a couple dollars at the dollar store. The most expensive item will be your fabric scissors. You do not want to skimp on those, so figure $25+. A spool of Gutterman 100% cotton thread will run you about $3 and needles will run you $1 for 12 (or $2 for the John James Big Eye needles). So total cost to start would run you less than $30 for your tools, plus the cost of your fabrics and batting. Patterns are available for free on the Internet.
Of course, I don't know anyone who wants to trace and cut out templates and fabrics by hand, and very few quilters I know do hand piecing. So you will need a self-healing mat, rotary cutter, and ruler to cut your fabrics. Then you will need a sewing machine and thread for sewing the pieces together. You will need a good pair of scissors and a pair of small snips for clipping threads. And you will definitely need a seam ripper.
Quilting is like every other hobby I have had. You get out of it what you put into it. I started quilting in 1999 with a sewing machine I had purchased in 1971 for $75. I bought good tools (a self-healing mat, an ergonomic rotary cutter, rulers with clear black lines [I hate the yellow ones] and good scissors) that weren't the most expensive, but weren't the cheapest on the rack, either.
You need to make a list of the items you need, surf the web and start comparing prices. JoAnn's and Hobby Lobby always have discount coupons. Check out the sale bins on Missouri Star Quilt Company and Quilt In A Day. Look at Amazon.com Be sure to figure in the cost of shipping, too. Some sites require a certain $ amount before they waive the shipping costs.
If you think this will be the only quilt you'll ever make, don't go to the expense of purchasing your tools if you don't have to. Find a friend who quilts and ask them if you can borrow their tools.