Dumbells - pick a pair that you can do 8-12 presses lying on your back, either on the floor or on an exercise bench (more range of movement). Keep your elbows tucked in, and your chest lifted up by squeezing your shoulder blades together (this is important as it puts your shoulder in a stronger mechanical position to avoid rotor cuff damage and loads the chest which is what you want - may seem over the top at low weights but is proper form as the weight goes up). At the top pause and concentrate on squeezing your pecs together and not letting your front shoulder move up. Tempo something like 3 secs lower, 0 at the bottom, 1-2 secs up, 1 sec squeeze pause at the top and back down again.
Once you can do say 3 sets of 12 then slightly increase the weight (small increments are the fundementals of progression) and start again. If your form suffers on a rep, stop, don’t force it or jerk it up. 1-2 mins rest between sets but aim for 1 minute as you get stronger.
Resistance bands - create a twist so the band is a figure of 8. With your hand holding each end of the loop, flip the band behind your back and take up the tension so that it sits at shoulder blade height. Then press your hands forward until they touch, squeeze your chest as above, and then slowly let your hands go back (elbows in!) and the pull your should blades together which creates a nice stretch/ tension in your chest, and then press again.
Progression is in reps, and then sets, and then higher rated bands. To be honest I do these as either warm up to bench press or as a ‘pump’ finisher after heavier bench press sets.
You can also do a ‘pull’ version with the band rapped around a leg of a settee or table and this makes sure you’re are working on the back and rear shoulders which is important to prevent problems with shoulders going forwards and an imbalance. I can explain the technique if you go ahead and buy bands but its basically a seated low row.
Rep on the minute - yes you’re shooting for 10 initially which will take 10 mins for each set. But say you can do 5 and then your form suffers then stop the set. After resting one day, then the day after you go again and shoot for 6 or more in good form. Then once you can do ten on the minute, start reducing the rest times between reps. Once you can do ten 10 reps as a continuous set then you can add another set.
Some people plateau at 5-6 reps and if that’s you then I have another strategy, from Russia (not drugs!).
Train or not to train when sore? - Classic question this. Soreness in my experience is a classic mental cop out where you can easily convince yourself that it would be counter productive to train and in any case you have no chance of progression. Actually you need to see what you do as training rather than competing with yourself. As long as you’re not so sore that you’re impaired and can’t perform reps properly its okay to go ahead and in many cases the increased mobilisation and blood flow will help speed up recovery - up to a point of course. Basically you need to be honest with yourself, are you crying off or are you actually physically impaired?
Also you need to force your body to some extent to adapt and that it had better hurry up and fix you back up because in 48 hrs you’re going again. If you always allow 72-96 hrs recovery your body will happily stick to this - remember frequency is a key driver of improvement and progression.
When I was in the gym and on rings and horse the pain the day after would be terrible, and was usually worse on the second day - this was a problem as my coach basically said that I needed to be tough enough to train 5-6 days on and only one day off. To get me there he made me train every single day at nearly full intensity for a month straight. It near damn killed me - I had to eat like a horse to cope, sleep 10 hrs a night and spend the mornings stretching and mobilising the sorest areas (no foam rolling in the 80’s!) and then spend 2-3 hours after school each night training through the soreness and pain. I wouldn’t recommend it, but it did work.
So anyway, short answer is you don’t need to be completely sore free to go again. If you’re so sore its impossible after 72 -96 hours then its better to reduce the intensity and volume to allow you to train more frequently - think about it in terms of maxing your weekly total volume.