Hey Bandit,
No need for a water pump but you have to do manual top ups. If you put a pump in a separate res you can pump in more juice and have it flow out of your grow container at the height you want it to stay at.. back into the separate res to be pumped again, it just has to be a little lower than the waterline of your grow container to drain down properly. I think it really helps to get more D.O. to your root zone, and more total water volume means more total nutrients and less issue with water disease, aka slime. Also much easier to add water or nutes to your res when you don't have to be fooling with the top the plants are set into. It is optional though, and you can go without for now.
The most important thing to ensure good growth in your system is to keep your water temps 62-68F. Going into the 70s will run the risk of the slime taking over your roots. Again the separate res comes back into play. If you put one outside your grow tent where temp is less, and had the water circulating in, it would run colder. I would maybe suggest using a cooler in the first place, as you can see with my pics. In the summer I have to put frozen water bottles in to keep temps in check, with buckets or totes it was always a losing battle, couldn't keep it cool.. with coolers, it's no problem. Again.. a separate res is handy so your frozen water bottle doesn't actually touch your roots, which wouldn't be good for them, you'd have to find a way to restrain or anchor it.
As for nutes I'd suggest technaflora. I've been using their recipe for success and it's been working really well for me, so well I don't even want to try anything else, though I might give ionic or canna aqua a go eventually, they are supposed to also be good in the DWC environment. When I first started I grabbed a technaflora starter kit, came with everything including cloning gel for $40. (though once it ran out I stopped using cloning gel, I don't even bother with it any more)
Rockwool is also completely optional, you don't need it, I don't use any. I take raw clones with roots and plant them into hydroton.