To lose fat, I find it best to do cardio in the AM ... and then weight train in the PM ... and mroe cardio after weights if you have too.

Your weights-free approach looks good to start from. When you are ready to add another piece of equipment, for about $125 I would add an adjustable incline/flat utility bench. This will allow you do do a variety of dumbbell exercises to hit chest/back/etc.

Hope I helped. If you need any other help along your way, feel free to ask me either here or e-mail/Private Message.