Building muscle and losing weight are competing goals. Since your goal is to lose at least 30lbs I would suggest you focus on weight loss as your primary goal.
Losing weight is 80% diet. Realistically, working out does little to help you lose weight.. but it does help you to maintain muscle and keep up your metabolism, so it is still important.
At 6'1" I'm surprised that you are only eating 14-1500 calories. I'm 5'3" and 1400 calories is how much I would aim to eat when I'm losing weight. It is possible to eat too little which will slow down your metabolism, encourage your body to hold onto fat, and generally work against your weight loss goals.
I actually do prefer to count calories so I know how I need to adjust if what I'm doing is not working. I don't like to guess, so the calorie counting works well for me. Beware the 'shakes' they can be fairly calorie dense... and they are a highly processed food.
As to your question about cardio or weights... both will burn calories. But if your goal is to change your shape and add muscle (ie. tone) then weights are definitely a better option.
Thank you so much for the feedback!
In terms of my calorie intake, the trainer I occasionally see said I should limit them for weight loss, which is fine, but I use myfitnesspal and it actually says I should have 1440, so I gave myself a little leeway there. I end up having two to three shakes a day because I'm not sure how to ensure I am having enough protein in a day otherwise. I need to have appx 80-90 grams per day, but beyond beans and legumes, I'm not sure how to get enough in my diet. I love eating raw, but I don't know that a raw diet and my current goals are compatible, does that make sense? I had thought that maybe I'm not eating enough, but I don't think that's the case. I make sure to have a good portion of healthy fats throughout the day, but maybe I should count them anyway to be safe and see. I started yesterday, much to the dismay of my brain.
My husband on the other hand asks if my clothes fit and if I feel good, the answer to both is yes. His reply is that maybe I should eat as I currently am and just let it all happen as it will. This seems logical too since I eat the way I do and workout as hard as I do. Maybe I should just trust my body to do what's going to do. As someone who has been overweight and struggled with self esteem pretty much always, I do feel much better since going vegan and especially since going to the gym. It's been about 8 weeks since I've been back at it hard core, and I can see cellulite disappearing and feels muscles coming in, the scale just isn't moving.
Thanks again for taking the time to read this! I'm sorry if it's full of typos, but I'm sick and in bed!