To give it a thorough cleaning, you will want to lay it down on it's face, on a bed or similar, unplugged. I realize this is not something you may be able to do on your own, but enlist a friend or neighbor for the two minutes it takes to move it off of wherever it is to do so. Then ask them to help you set it back where it was when you are done.
If a vacuum doesn't get it deep cleaned enough, and judging by the amount of junk in it, it likely won't, then you really want to pop the back panel off the TV. A dozen or so screws is all it takes. This should give you clear access to blow out dust and to fully vacuum and clean everything properly.