As the Dad of an 18 year-old who started cycling very young I can confirm that you definitely do not need a power meter.
However there is a significant difference between you and an oldie like me; your body is awash with testosterone meaning that any training you do will be quickly rewarded by muscle growth although you must take care not to overdo the exercise in limited muscle groups. Cycling is very specific in the muscles it exercises because you are clamped rigidly into a machine, which controls your leg movements precisely so you also need to exercise the muscles that give support to your ankles, knees and hips. For this I suggest some walking on rough uneven ground; if there's a steep hill near home go and walk up and down that a couple of times a week. Walking will also be a good refresher to stop you feeling stale with cycling - look after your mind as well as your body.
Joining a club is a good idea as you will be mixing with older riders and learning cycling lore and wisdom from them. Go and buy a small book called The Escape Artist by Matt Seaton, which you will love reading as it's the story of a young man who became obsessed with cycling.and it explains a lot about cycling etiquette and has the best explanation for leg shaving. It's a true story and has a tragic twist at the end.
Out riding you will have less stamina than older riders but you will be a vigorous climber and sprinter, especially as you probably only weigh 50 kgs or so. Be wise, shelter in the pack, bide your time and then be near the front for the final sprint to the cafe, which you will win easily. Make sure your cleats and pedals are set up securely because my own son has crashed twice when he has come unclipped during big efforts. Learn to look after your bike, keep it clean and take pride in its mechanical perfection. Change tyres and brakes that are less than perfect.
Be aware that your body is using energy to reproduce cells and grow, so you need lots of sleep and good food. It's no use getting up late, necking a bowl of cereal (which is basically starch coated in sugar) then going cycling; you will have missed the most important meal of the day and will be one meal down on your buddies as well as being fuelled only on sugar, which will burn off in an hour. Go to bed early, turn off the phone or tablet, get up early, have a good cooked breakfast with carbs in the form of brown toast or porridge and protein in the form of eggs and bacon, then go cycling.
All of this advice is what I have learned from seeing my own son struggling with energy levels.