congrats! first, sand prime and paint out those cabinets....i'd go with a grayish shade of white or pale gray that will work with the flooring. i'd also carefuly chip off the yellow tiles. since on a budget, consider applying some beadboard as your backsplash, painted in a glossy, oil based or marine paint in a crisp white to keep it scrubbable, then, dress up the edges with some small mouldings, painted in the same white paint. this is going to be SO MUCH less costly than tile! and it will look great with the butcher block countertop. you can probably refresh the butcher block with a light sand and oiling. you could even get an additional piece of butcher block (ikea) and create a step-up 'bar' for some stools on the peninsula for some casual seating. then get a pair of pendant lights to hang from the pot lights above (they make lights that insert directly into the pot light...no hardwire necessary).

Maybe a cream so the eye is drawn to the interesting table pattern and not on the splashback?

You could install racking for both sides of the room, toys & clothes that aren't being used can go into large plastic containers with lids. The two bikes could be hung from the wall or ceiling. And yes, anything that doesn't need to be there, move it on. There are so many hooks and storage options available that it would be very easy to sort this out and by getting a lot of it off the floor.

Why don't you live in the house for a while and get a feel for things. The curtains are bright but if they are still good quality / newish it would be a very expensive exercise to replace them (I have just spent a few thousand just on three rooms), you can always add a few red cushions or a red toned throw over your existing couch or a rug with a red tones in to it, to tone the red down, if required. Repainting the walls is cheaper than replacing curtains and a piece of art with red tones may also help. As far as furniture is concerned it would depend on what you like style wise. Why not send us a photo after you have moved in. You may find some of your concerns disappear once you are in and settled.