Such a timely post, as we are looking at redecorating our basement ... which is a result of us installing a pool and the access is through the basement walkout *sigh* ... talk about scope creep!
I agree with the consensus that this decorator does not sound very helpful! She should be helping you with your stated objective (freshen the floor and walls of the basement), not piling on a bunch of projects that you weren't interested in!
I also agree definitely start with the flooring and then do paint ... paints the easiest bit and there are so many colours you can definitely find one to go with your flooring choice. I think you don't need it to match to upstairs per se, but you definitely want flow if the two spaces are visible to each other ... so a stark shift in colour or tone will be a bit jarring.
As to flooring material, I think your babies are younger than mine - to date, we've gone with a rather industrial-strength berber in the basement. This kept the floor warm (our basement being a walk-out is cold in the winter) and more absorbant of kids running around, tumbling, etc. and have barely worn and it must be close to 10 years old now.
We are going to change to a laminate when we re-decorate, since it is equally durable (and better for wet pool feet). There are some super-nice laminate options out there so that's another option to consider if you like to look of hard-wood but don't want to worry about Hot Wheels car scratches, etc.
Your blonde hardwood and the clean simple finish of the railing post etc. makes me think Scandinavian ... you could look up Scandi design for inspiration if that style floats your boat! Light and bright for a basement, which is also nice in the depths of winter!
Keep us posted; I love this stuff!