You can certainly use your Brother sewing machine to quilt. Your only limitation is how much quilt you can push under the arm of the machine. Keep in mind that the maximum amount of quilt that has to fit under the arm is only half of the quilt, as you can always turn the quilt around to do the other half. The method I like is to create large, loose pleats in the quilt while feeding it under the arm.
In my opinion, the easiest way to quilt is to use a walking foot to create wavy lines across the quilt. There is no need for precision for this method; you simply move the quilt sandwich somewhat to the right and left as it feeds under the needle to create the waves. You leave the feed dogs up. In general, a walking foot designed specifically for your machine is best; however, sometimes generic walking feet will work. A lot depends on the compatibility between your machine and the walking foot.
Here is a website with a video tutorial on how to use a walking foot to create wavy quilting lines:
http://www.bijoulovelydesigns.com/20...-tutorial.html
And here is a website with more advanced wavy lines looks:
http://www.quiltingismytherapy.com/m...lting-designs/
Also, if you Google "wavy line quilting" and then click on "images", you will see examples of quilts made with this technique.
You can also quilt straight lines with a walking foot; however, straight lines require more attention and precision. Placing long strips of blue painter's tape on the quilt is helpful for creating a guide.
A different approach to quilting is free-motion quilting. This is the method that requires you to drop the feed dogs and use a darning foot or "jumping" foot. This is a more difficult technique to master, and you would want to practice on a scrap quilt sandwich before tackling your first quilt.
How to plan to baste your quilt? My recommendation is spray basting (505 is the best brand I have used) because it creates a uniform "bond" between all 3 layers of the quilt sandwich, making it easier to quilt without getting puckers or tucks. I also recommend starching both top and backing fabric before layering (stabilizes the fabrics). Cotton or 80/20 batting is good to start with as it does not slip and slide the way a polyester batting can, plus spray basting sticks better to cotton than to polyester.