Your hang out/reading space sounds like a worthy goal! What a great reward to look forward to! I really like your slow and steady method. I'm hoping that doing things that way will keep things in check. As I keep going around doing little things, it won't get a chance to build back up more than what we need and use.
I had to really learn how to keep flat areas clear. For a while I put notes to myself on the counter. This was hilarious. Even now, if I put something on a counter for just a minute, others will follow suit. Instant "hot spot" (Flylady says). Thankfully DH was always on board. He did seem hesitant at first, but now he loves it. I didn't like moving everything to clean the counters so I asked if we could take everything off. Now I can just wipe things up right after every meal in a matter of seconds. The children were able to help sooner without needing to lift a heavy crock pot. For the mail, we write the date on the envelope of anything that needs action and stick it in a large plastic envelope. Then we sit down to empty it when we have time to dedicate to it. We have a shallow drawer for any catalogues, ads, or coupons we want to flip through later. I have to remember to get to it or empty it!
We still have a lot of stuff, and we will have a lot of it as long as the children are home. I love that they can have so much fun and creativity and loads of books. I want to make sure they can easily find and enjoy it all.
I'm pretty sure keeping things clean is more important than tidy. I prefer tidy as long as everything is reasonably clean. The bathrooms and kitchen get a quick wipe down every night, dishes are done, and everything gets a weekly cleaning. It's the things like scrubbing baseboards I'll delay on in favor of keeping things tidy though.

Quicker cleaning is a huge motivation for me to have our spaces clearer. Have fun getting ready to enjoy your new quiet space! It sounds heavenly!