I'm glad you are thinking about this but it may well take time for you to take that step. I've been vegetarian, often vegan, for nearly 20 years. Like you, I made this decision for animal welfare reasons. I think it's natural for people to eat meat, but I don't need to in order to fulfull my dietary requirements and so I don't. It's the intense farming methods, and some slaughter methods that made me decide to become a vegetarian. That said, beef is probably the "kindest" meat you can eat, and fowl and pig the "cruelest". If you want to change the way you eat for animal welfare reasons, increase the beef at the expense of pork, chicken and turkey. The dairy industry is not kind to animals, especially to male calves that are not intended for veal, so it's fortunate that you don't like milk - though you may well like cheese. I found cheese the hardest food to give up and I still buy goat cheese a few times a year.
It really is a big step to take and it's quite a shock when your body feels out of order for a few months as it adjusts to the changes. Once the change is made, it can be a very healthy diet. I don't take iron, or B12 or vitamins, but I always come out of my annual check-up with high marks. No anemia, and fabulous cholesterol results.
Becoming vegetarian is a very personal decision and you should think it over carefully, read a lot about the lifestyle. Little changes can be made over time. I remember that I gave up meats one at a time and it took a few years to give up shellfish, which I adored. I worked recently (I work at a university) with a young woman who thought about it for about three years before deciding to become vegan. She's a musician, hard rock, and it's part of her Straight Edge profile, but she had to take her time over making the change.