Oh a serious exerciser! Excellent. I'll give you a few tips from the research I did on myself see if any of it works for you too.
When in the gym, doing legs will cause the biggest sugar drop (it's massively energy intense).
Rep ranges of 8-12/15 will cause you low sugars, so make sure you have your dextrose tabs handy. Check your sugars before you start and about 30mins into it too as well as post workout. At least until you get used to how your body responds.
Rep ranges of 4-6 don't cause any sugar shifts (it relies on creatine for the energy rather than glucose).
I avoid too much CV it makes a mess of things for me and pushes the sugar levels up. If doign the 8-12 rep range I will do about 4-5mins on the bike first to push them up before switching to weights (which lower it).
Don't exercise if you are above 11, you risk flooding your system with ketones, and avoid it too if you are below 4.
Remember the stretching!
If you are going to use supplements protein is the best one to get going with. Start with a 20g-30g, see how your body reacts, thena few weeks later you can up it by 10g and so forth.
Caffeing will stablise the sugars during your workout, so a good coffee (or two) should do the trick.
Because of the muscle glycogen reliance for us type 1s for energy you will grow much faster than expected, this tends to stablise the sugars.
Also keep in mind that we take longer to heal, so muscle damage during a workout needs proper recovery, at least avoid doing gym work the following day.
When you get into things more, if you are going to supplement with anything else I have found that Alpha Lipoic Acids are great (they increase the body's efficiency at muscle glycogen use and recharging), and BCAAs. I personally avoid creatine which at your age I would strongly suggest you do too, there's no need for it and it puts more pressure on your kidneys which we don't really need.
Hope that helps, and do make sure you tell someone at the gym (a member of staff preferably or a training buddy) that you have diabetes and if you hypo they should give you some lucosade. Just in case.
Do let us know how you get along

The plus side is that in the long term the more muscle you have the better your sugars and hormones will be balanced and the less likelyhood of diabetic complications.
Frankie