Yes.  Attend the Mat Tutorials as often as you can.  Once you learn the exercises you can do them at home and come into the studio on occasion to learn new ones or to fine-tune the ones you know, or attend Mat Workouts.  Do keep in mind, however, that Pilates is a system of exercises.  Using just one part of the system may limit your benefits.

Can I do just the "machines"?

Realize that Pilates is a system of exercises, and eliminating one part of the system may limit your benefits.  You may need some of the mat exercises for your body.  Besides that, it's good to know your Mat workout in case you cannot come in to the studio or the studio is closed.

You can, if you want.  But you don't have to.  Authentic Pilates is safe for almost everyone, regardless of age, fitness level, or injuries.  This is why the instructor training program is so extensive.  Your instructor chooses the exercises for you; it is rare that a novice is unable to do ANY exercises with equipment.  If you have a specific medical condition or injury and are unsure, it doesn't hurt to ask.

There are instructor shoppers out there who may be able to help you (one of my clients is).  Talk to your friends.  Word gets around, good AND bad, true AND false, but maybe you will get lucky.  Or check the internet.

When you find an instructor, check his qualifications.  Don't be impressed with nice-looking facilities; a good Pilates instructor can give you a great lesson with very limited equipment.  A studio doesn't have to "have it all" to be a great studio; it requires one thing and one thing only: a great instructor.  Find out where the instructor trained.  Training could be interpreted as having attended classes or having taken private lessons.  You want to know if he trained to TEACH Pilates to others.  Ask specifically if he is certified.  There are instructors out there who go through a program and set up a studio, without completing their programs or passing the tests.  Find out how many hours he spent training to teach.  Typically, a program has seminar time where material is presented followed by 600+ hours of observation and practice teaching time.  At specific points in the training, one must take tests, and must pass a final test to get a certificate.  If he doesn't tell you, he is hiding something.  If he does tell you, get confirmation.  Call/write/email the training center and find out if the instructor is on their list.

If everything checks out, try a few sessions.  Did you learn anything new about how to move your body?  How did you feel after each session?  Did you get a warmed-up, loose, worked-all-the-muscles-in-my-body feeling?  Did you hurt anywhere?  Ask yourself if the sessions were worth the money you paid for them.  Do you get as good a workout doing another kind of exercise?  If so, then perhaps your time and money is better spent doing that other exercise, or find another instructor.

Many people with injuries try Pilates because they hear or read that it is helpful.  If you have aches and pains, did you find it helpful?  Did any of the exercises cause pain?  If so, did your instructor gloss over it and ignore your complaint or did he ask you more about it and try to fix it?  Did your pain improve or worsen with the next session, and the next?  No matter how nice your instructor is personally, you have to look out for yourself.  Try someone else.

Can you motivate yourself to exercise on your own?  If you can, then another option is open to you.  Make time to take a lesson once a week for 3-6 weeks with a good (even if far away) instructor.  In between these sessions, practice on your own at least 3 times.  Memorize the exercises.  Write them down.  Draw them.  Remember the corrections you are given for each exercise.  Practice, practice, practice.  When you have made a habit of doing your home exercise program in 15-20 minutes 3x a week, you can cut back on your lesson frequency to once every 2 weeks.  If after a month you are still exercising ON YOUR OWN 3 days a week, try monthly lessons.  Sure, you can stop taking lessons at any time, but oftentimes seeing your teacher once or twice a month keeps you inspired enough to continue exercising on your own 3 days a week.