I started my journey with exercise alone. At that time I wasn't ready to change my eating habits and I really just wanted to focus on my fitness levels initially. Eventually I did making small changes to my diet but it was never all at once and I did it gradually because it was much easier on me.
I think the best thing to do is make changes that you CAN stick to. I've never been successful with calorie counting because it actually made me hungrier (because I kept thinking about food). It was easier for me to give up certain foods or introduce new ones and pay attention to my hunger cues then calorie count.
In the end you have to do what works for you. If you CAN workout now do it! Make that habit and then start worrying about the rest.