Let's get you up and running on terminology and a pinch of encouragement:
Read lips = Speech Reading
It is okay to say you are hard of hearing (HH) as that covers much territory and can mean much too much. So, in your case, it is okay to use that description for yourself. There is nothing wrong with its use (many people as they age, will lose some hearing, so it happens to many (my father was one of those--and was most frustrating since he refused to learn sigh, and ALS was often my best means of communication, but, also, I rely heavily on Speech Reading to "fill in the blanks").
When you get to about the 3rd level of ASL, you will encounter compound signs (e.g. "know-that") which will open up the world of communication even more.
Most people as they start to learn communication, start off with finger-spelling, then add ASL signs.) I think you will find that many people are forgiving of your mistakes and many will be helpful (my best friend says he taught everyone around him, sign so they could take with him--which is fairly true for a lad who was the only deaf person in the town.) Like anyone who is learning, there are levels of fluency (I have the communication skills of about a 12-year old, so I can't really hold a detailed conversation, but I can communicate--I came to ASL late as there was nothing available near where I lived.
Remember to have fun....
