Welcome to the forum NordicSplitter.
That is a good mix of wood you have and I'll second what gzecc wrote.
Most wood should have about a year after being cut to length and split. Wood doesn't dry much at all until it has been split and then it is best to stack it out in the open air where Mother Nature can help you. Wind is your friend. This being your first year I would also recommend stacking the wood in single rows. We usually stack about 4 1/2' high and that should decrease to around 4' high by fall. The reason for the decrease is a good deal of the moisture has evaporated. But oak gives up its moisture very slowly. Don't cover the wood this summer. The evaporation of moisture will be better with it uncovered. Don't worry about rain unless you get rain every day like in the Pacific NW. We leave ours uncovered until just before the snow flies and then it is important to cover only the top of the stacks.
I would burn the silver maple and cottonwood in the fall. As the weather gets colder then move to the cherry and elm. Then as it gets cold move to the ash. The apple and black locust would be saved for night burning during the coldest part of the winter.
Should you start on next year's wood? YES
!! When you get next year's then start on the following year's wood. 2-3 year ahead is ideal and also remember that oak needs 2-3 years before it is burned.
Do you have enough? More information would be needed to answer that question. You might also consider editing your signature line and put in there some information, like what stove you have, maybe your saw or saws and how you split wood, etc.
Again, do you have enough? What size is your house? What stove can also mean a lot. For example, we used to burn 6 full cord of wood per winter with more used in hard winters. When we installed the Woodstock Fireview our needs decreased by 50%. We've had that stove 4 winters now and used 3 cord each winter until last winter when we went a bit over 3 cord. This gives you an idea on how stoves can make a difference. Of course insulation and cutting down on drafts make a huge difference too.
Good luck and we hope you keep posting.