For strength training you can go mild if you use resistance bands instead of weights, they can still scale up to serious weight training too if you need but it is a lot safer with bands for those with issues, I can't cardio anymore but I can still do some strength training which is at least retaining some capacity to move around without PEM. I got a set of 4 bands (brand is coregain) to replace the dumbbells/barbell as my ME got worse and have been able to gain muscle without the injuries. I found my strength varied a lot day to day as the ME got worse and that meant a lot of changing the weights on my spinlock dumbbells and a lot of under and overweighted training difficulty. I also found I was getting injured a lot, possibly just from putting them down but also positioning to get the weight right was an issue, up and down off the floor all the time etc. Bands have proven to be a lot easier on the body.
To use bands I have to modify the usual strength training regime by keeping a solid eye on heart rate and stopping if I can't stay just about below 60% for a set of 10 reps. I wait for my heart rate to drop to baseline while resting which typically takes 3-5 minutes between each set. Normal weight training is about 30- 60 seconds muscle under tension and then 90 seconds rest. I have had to shorten rep cycles and take much longer rests. I don't think you can safely do this with ME/CFS without a heart rate monitor and knowing where your likely maximum is (don't get me started on 220 - age, quite possibly the most misquoted fitness paper of all time) but if you start mild enough you can likely work out what that point would be anyway, it's not like 60% is a magic switch point. I am mid my Set A right now, I read, write and watch TV in my rest periods and I am not very strict with how long rests are, I am trying to relax and return my heart rate that is the point of the rests. Takes a lot longer than a typical strength training however, you will spend hours doing what a normal weight trainer could do in 20-30 minutes.
My heart rate will gradually climb as I do these exercises and once resting doesn't get me down to a certain point I have to stop or risk PEM. Bands allow you to go easier than weights and are more progressive and mirror the bodies muscle strength profile better than weights. It can be done at home but for ME/CFS sufferers the advantage of just being able to let go and stop exertion that instant is a pretty big plus point if you set a heart rate alarm. The very small variances you can make to the difficulty also make it easier to adjust without needing to constantly adjust the weights like with dumbbells. It is quite practical and since you are stretching a band you can do it standing up or all laying down if you have positional tachycardia, its a lot easier to adjust to something that works since you don't need gravity to make the exercise work.
James Grage is a bodybuilder and the guy I think that started the use of bands like this in a big way, he is the place to look for training regiments and how to do it. His
tips and tricks video is a good place to get started with what you need (band type and gloves). The total resistance workout on
paddleboard turns out to be a good starting place to learn the first exercises for each area of muscle. He has videos that go into particular areas, chest, arms, back and those are great to watch too especially if you can't do one of the paddleboard exercises with the lightest band you have. He has some (door) anchored variants that can be done with less strength for all the areas he is talking about and while tension all the way through the movement is optimal we are sick people so if it's loose and you peak at contraction point of the muscle you will still gain strength from doing it. He isn't focussed on ME/CFS, the guy is an ex-professional bodybuilder. But it turns out his exercise regime adjusted a bit is quite doable for me at least.
I haven't personally found any energy gains from doing resistance training, but I am stronger and that has helped me just move about and doing various activities. I would say be cautious, do just a few reps just the once to begin with and work very slowly up because the last thing I want to be is remotely responsible for a crash from this. I have crashed from this training before I worked out my limit and it was deeply unpleasant, the worst crash I have had.