Hi, I am far from an expert, and I am not in that good a shape myself (but working on it right now, I have a 23 km run of mix running and bike in 2 weeks lol), but here are the best recommendations I can give you based on my experience and knowledge:
1. Don't do a real diet to lose weight. What you should do is only to eat healthy things as much as you can and cut the obvious sources of extremes fat/sugar (you know them, but basically fried stuff, rich sauces, meat with too much fat and things with a lot of sugar). BUT, eat pretty much as much as you want without exaggerating, and maybe try to lower that amount a little but do not get hungry. If you are hungry, try to fill yourself with vegetables and fruits (fresh/raw if possible). Anyway, if you want to lose weight on a 5 months objective, the best is to go slowly, else it's bad for your body. The best way to do that is to cook yourself, eat as much fruit and vegetables as you can and do the obvious. For example, I replaced most of the red meat I eat with horse meat because it's much healthier. You can also try to eat more rice, quinoa, etc., they taste good if cooked well! Also, after a training, drink a small chocolate milk (just after). It gives back to your body some sugar and proteins. There are other stuff that can do the job, but chocolate milk is easy to find and a good one. You should drink it max 15 min after a workout.
2. Train everyday or almost if you can. In the end, the more you train the easier it gets. It's all in our head that it is difficult, not on the body (well maybe a little for the first week). I KNOW that it is hard to get motivated to the point to actually do it, but the best way that I found to train on a regular basis is to simply make it a routine and force yourself to keep it a routine. Force yourself at the beginning, then set yourself objectives and force yourself to achieve these objectives. Like I said, it's all in the head since you will find quite fast that at the end of a training you feel quite great. If I was you, I would use this MS150 as your main focus and force yourself to slightly increase your training everyday (I started with only 20 minutes of stationary bike and now I do more than an hour, after a few weeks, and I had harder weeks). Perseverance is the key.
3. If you want to train your muscles to be good at something, the best way is to do that something. So basically, if you want to be good at climbing with you bike, well climb with your bike as often as you can. The reason is quite simple: You body will develop your muscles in response to their usage AND you will also develop your nerves in an optimistic way for the movements you do and THAT is more important than your muscle mass. Ever seen a culturist swimming? It would be too funny
. For sure you could also do some gym training to complement your bike training and help develop your muscle, but I would focus first on training with you bike and train in a gym as a complement if you want it.
Hoping it will help you! Good luck with this MS150!