So the days I don't do weights, do the cardio then?
Your focus should be on weight resistance training right now, not cardio. You don't need to lose weight, you want to gain lean mass.
That means:
1. weight training (start slow like I said)
2. a modest increase in calories at first, more as you increase your number and intensity of workouts over the course of the year
3. eat clean. high quality protein (grass fed beef, organ meats, free range eggs), moderate carbs (preferably minimally processed), high quality fats: avocado, salmon, nuts, etc.
Enjoy a bit of high quality dark chocolates, unsweetened organic iced tea, get some fresh organic veggies directly from a farmer's market, not the grocery store, not even Whole Foods.
Take a high quality daily multivitamin. Get bloodwork to see if additional supplementation is beneficial. A VitD supplement is good in the winter/early spring.
4. cardio for me is a fun sport: basketball, cycling, soccer, hiking, walking, any sport you enjoy. Get good at a sport for fun, not to burn calories. You are already well below average in weight (assuming you are close to average height).
Join a meet up for young adults and go on a hike or canoeing or something fun. It's not all about work work work.
Honestly, I'm 10 pounds overweight, and have been as much as 35 pounds overweight in the past. It made almost no difference in my ability to attract women. I'm not saying being in top shape doesn't help, it does, but the difference is surprisingly modest.