Jelman.
Hello and welcome to your new lifelong learning extravaganza, like many on here I have been going this gig for a very long time and still learn something new everyday, what really is the plus is that your son wants a hand in it too that’s great we need fresh blood in this blue collar field.
Now your lathe, there are volumes written on just this one procedure alone and it important not to get carried away with this task. Paramount importance is the lathe be level two dimensionally (X,Y), the lighter models (ie bench top lathes, mini machines etc) have a tendency to flex and twist easily due to their lack of structure, heavy floor models (lathe which rests on a factory manufactured table or cabinet) are not as picky and are really your friend in the end due to weight and build (construction).
By the sounds of it you have a floor model with some weight that’s good and you have mentioned the floor is concrete ok so far so good this is what you need to aim for with your situation, you don’t necessarily have to bolt but bolting maybe an advantage for the leveling process, each foot will require a shim block and or blocks ( or at least three will ) these are nothing more that little slabs of steel of different thicknesses like a set of auto feeler gages just square or rectangle, it could be anything as long as you have a wide range of thicknesses to buttress up your feet while leveling, they must be steel or some metallic compound the reason is they will not decompose and loose there integrity and compress like wood would.
The rubber is fine and some say its great for vibration purposes but not a given, I have my own 800lb lathe sitting on thick rubber feet with shims slotted on top only because my floor is 12” thick concrete and sometimes retains water and I did not want that water eating my feet or shim stock.
Through the leveling process if you were to bolt through the foot and shim stack where ever that foots rests under pressure it will stay, so like I mentioned bolting would be an advantage.
Now we have the means for blocking and seating the lathe structure to the foundation you will need to level the beast, puritans will say you need a machinists level (highly sensitive spirit level) but since such a tool would cost three quarters of the purchase price of your lathe, get the most sensitive level you can afford, you can buy now these digital levels that give you angle readings for a really reasonable price and they are themselves of high accuracy and will do the trick. Also this is a great item to have in your tool collection as it will be used for all your future machinery needs plus the old ladies picture hanging requirements.
The reasoning for leveling a lathe is to eliminate all side forces and irregular misalignments that will transmit its distortion into your work and may cause damage to your machine.
The actual technique for leveling a lathe is posted on this forum and is widely written about on the net so 5 minuets of you searching will turn up the how to on it, all I want to add is that whatever procedure you choose really understand what your trying to achieve, as in the future your measurements or results may be off and this maybe a reason, but do not get bogged down too much with all the micro annalistic written tutorials on it the essence is simple straight and level in two dimensions(x-y). I have drawn a sketch giving you the basics of what you are trying to do. On the sketch it shows what is the (X,Y) planes are, twist and camber, that’s it!. These are the right terminologies applying to all machine tools so now you know what we are all talking about.
It took me about three hours to level my lathe to get it tweaked in, this was a process of using the dial indicator, level and a test bar, (all of which you will learn through whatever tutorial you read), in fact just by installing the lathe you will learn a lot about machining and the essence of it, getting as close as you can will serve you well in the future.
All in all this is a fascinating rewarding hobby, its builds character and keeps the brain healthy, only as you dig deeper into it and need advice from forums like this will it come to you, keep it simple, don’t over analyze and enjoy. Revel in your new adventure best of luck!!!!! Anthony.