There is a certain aspect of adaption when doing any new type of exercise. Your body is aching because you have introduced it weight training and it hasn’t adapted to it. If you were happy with the volume of your training before adding the weights then I would stick it out and see how it improves in the following weeks. The DOMs should go down dramtically.
As to nutrition, you should have protein, good fats and carbs post workout. Full fat milk (all other milk is marketing guff in my opinion!) has an excellent nutritional profile is should be a staple. Your body needs to recover and you need to fuel that. How much you eat is up to you and what your aims are, but that’s a whole other topic.
Creatine is a useful supplement for strenth/speed athletes. It allows for slightly better muscular endurance and recovery, eg the ability to get one or two more reps in. There have been hundreds of studies done on it and it does have a positive, if not profound effect. The main side effect for cycling would be that it causes the muscles to retain more water, hence weight. Some people don’t see this as a side effect as it can make muscles look slightly more bulky and good for the mirror….