Hey Trish! That is a pretty adventurous goal but as someone who has been sewing longer than I can remember (almost) I say go for it!
In looking for a first machine here are some thoughts:
First, make sure you try them out. There should be a local sewing machine dealer where you can go in and sit down and try them out. Ideally they will have fabrics of various types so you can see how they work in a variety of situations. Tell them up front you are beginners!
Second, keep it simple. Unless you plan to get into art work quality machine quilting or high end machine embroidery, there isn't much you can't do with the basics. What basics? There should be forward and reverse settings, straight and zigzag stiches, ability to vary length of stitch (and width for the zigzag), bobbin winding, button hole setting, and that's about it. (Other sewers am I missing something that is so basic it is not even registering on the radar?)
Third, think portable. Something you can tuck away into a closet when you aren't using it. Personally, I don't like machines in cabinets anyway because there is never enough work surface around them.
Fourth, look for solid construction. Singer has always made a pretty sturdy, simple model. But then again I have a couple of Elnas I have used literally for decades.
As for how do you learn to sew, well you learn most by doing. But having said that you do need a teacher of some sort. Do you have a friend that sews that would help you? Or check out the local community education program. In our district we had a great adult enrichment program until the morons that run our district decided learning to sew was no longer an important skill so they dropped it from our Home Ec program and sold off all the machines! But I digress.
Often sewing machine retailers offer classes. Something to ask about when looking at machines.
And don't overlook estate sales! Once you've played with several types of machines at a retailer, you may want to check out estate sales (if they have those in your area - guess I shouldn't presume that!) or the classifieds in your local paper. You may be able to pick up something decent but used at a much lower price than if you went new.
And a DD that wants to do this at 11 may lose all interest in a year or so. Mine has a pair of pajamas cut out and sitting in my work room for 2 years now. So far I've refused to finish them.
Just ask if you have any other questions!
Deb