I would say $100 to $200, depending on what sales you can find. If you're already a sewer and just moving into quilting, then your biggest expense will be buying a rotary ruler (I'd start with a 6 1/2" or 6" x 24"), a cutting mat (18" x 24" is good) and a rotary cutter (the 45mm size). Joann's has a combo pack with these in it that's probably $20 or $30 on sale or with a coupon. As a prior sewer, you would already have a machine and general sewing supplies - marking pens, seam ripper, scissors, pins. You may also want to buy a walking foot, which helps greatly with straight-line quilting and attaching the binding. These run $30 to $80 or more depending on your machine. So a prior sewer transitioning to quilting would be out $50 to $100 not counting project specific supplies (fabric, pattern, thread, batting)
A brand new sewer starting from scratch needs the rotary cutting kit and walking foot recommended above, a sewing machine, and basic sewing supplies. If you watch thrift store/yard sales, you can pick up a great used machine for under $30 or a basic machine new runs around $100. By shopping sales and/or using Joann's coupons, you can get general sewing supplies (seam ripper, scissors, pins, marking tools, etc.) for probably less than $20. So a brand new sewer would be out $100 to $220, not counting project-specific supplies. This would be a machine & walking foot, rotary kit, and general sewing supplies.
Project specific supplies vary based on what your going to do. At the very least, you need fabric for the front, fabric for the backing, batting, thread, and a pattern. Patterns can be found for free online. If you already sew, you've got thread you can use, if not, you can get basic thread for just a couple of dollars (I use the Coats & Clark stuff). Depending on where you shop, fabric can be as low as $3/yard (using coupons/sales) or more than $10/yard. Let's say you're doing a baby/child's quilt about 40" x 50" - you'll need about 4 to 4 1/2 yards fabric for front, back, and binding, plus a crib size batting. Shopping at Joann's (sales/coupons), fabric & batting will cost you about $20 to $25.
So if a brand new sewer, you're looking at $120 to $245 to purchase your supplies and complete your first project (a 40" x 50" child's quilt). A sewer transitioning to quilting would be out $70 to $125 to do her first quilt.