What should my goals be focused on?

So I am a 5 feet 11 inches male who is 18 years old; that last time I checked weighed 125-126ish but after today realised that it is less with my doctor telling me I weight 122lb (with clothes on) and then when I weighed myself on a scale I just recently bought I weighed in at 120.8lb (with some lightweight gym clothes on) so I am realising now that my weight is 120-122lb which I feel might be a bit low. I have already received feedback on needing to gain weight (will post pictures of my physique of about one week ago it's more or less accurate for the time being). I did start a new lifting program that is a 3-day set of full body suited for beginners (even though I've been lifting for about 8 months but did not lift with a proper program) I do cardio about 3 times a week that consists of jump roping for about an hour but did not jump rope two days of the week this week as I felt it may not aid in building muscle but did miss it and felt weird without it.

Considering I weight 120-122 I do not think I could stand to lose anymore (not that I could I think) but not sure how to go about increasing how much I eat to account needing to gain weight and to fit my jump roping lifestyle. I need some advice as too how to go about this?

Also I do prefer to do fasted weight lifting and cardio whenever I can meaning as soon as a wake up working out and then eating my meals throughout the day. When I can't I eat breakfast then lunch and usually workout within 4 hours of eating lunch. Is it recommended to do this with my weight or can I as long as I am eating in a surplus the night before?

Cheers all!