When I was in college myself and my friends made loads of shirts, pillows, pillowcases, etc by doing what you were originally talking about using iron on material.
The iron on stuff we found that worked best to attach the fabrics together was
Heat and Bond Ultra it is available at Walmart or any craft type store. Not regular Heat and Bond and not Heat and Bond lite. Well you could use those but they do not hold up as well as the Heat and Ultra. I made many shirts using this and they held up to many washes.
What I found worked best was to wash the shirt without fabric softener and dry it without dryer sheets. They both put a coating on the fabric which prevents the fabrics from making a complete bond.
Cut a piece of heat and bond to a similar size to the shape you will be cutting out of it. But don't make it the exact size. You will iron this to the wrong side of the fabric you will be using. You can cut the fabric to a similar size of the Heat and Bond or just iron it close to the edge of the fabric. Make sure the fabric is smooth and wrinkle free before you iron the heat and bond to it. As for how long to iron the heat and bond and what temperature follow the directions on the package. I don't remember exact details but the package directions are good. If the fabric is not sticking together you need to iron it more.
The side of the Heat and Bond you iron on has a white surface which you can draw your design you will be cutting out. Remember you need to draw on the heat and bond in reverse as you will see the opposite side. The reason you ironed the heat and bond to the fabric before you cut the design out of the fabric is because it is much easier to cut the fabric with the heat and bond attached plus it keeps the edges from unraveling.
Once the design is drawn onto the white side of the heat and bond, you can cut your design(s) out. Once you have everything cut out, lay out the pieces to get an idea of how things will look.
When you iron the pieces on, you will start with the pieces on the bottom. You need to remove the white paper off the back of each piece of fabric and iron it onto the shirt or item with the good side up. I remove the white backs as I am ready to iron them on, in order to prevent accidentally ironing things on at the wrong place.
Keep ironing on the various pieces on top of each other to create your design. You may want to buy some parchment paper (not wax paper) in order to put over your design as you are ironing it together, this will prevent your iron from getting sticky, if the heat and bond is out of the fabric.
Here are some samples of things made with Heat and Bond Ultra.
The white shirt was made using the heat and bond, the other is a professional made sorority jersey. The letters on the white shirt were outlined with fabric puffy paint. You can use the fabric paint if you chose. I really don't know that it makes all that much difference as to holding the design together but it covers up the fabric edge.
The turtles were pieced together how you would make whatever design you would want. Notice the fabric does not have the fabric paint on the edges.
A few other Heat and Bond projects, the woman wearing the black dress is holding a wooden paddle it is not made with heat and bond
Once the item is made you can wash it like normal, however dry it on low in the dryer or hang it up to line dry in order to make the designs last. You can put them in a high heat dryer but they won't last as long, so if you want the designs to last use the low heat or hang them to dry. If you dry in the dryer , especially on high heat don't let them sit in the dryer after the are dry as the designs may take the shape of whatever direction they are lying.
I hope this helps. If you have any questions let me know.