Huge Lego fans here.
I also recommend the storage bags for Lego, and duplo for that matter. We got the one from Wilko for about a fiver. Also drowning in Lego here. For a first try with building I'd go for a 4+ Lego city vehicle because they're fairly simple to build and have good playability once done. It didn't take long for my DS (4) to progress to bigger and more complex sets, and now we but pretty much anything. The only thing he struggles with are the technic elements in some of the more complicated sets. I'd also recommend getting an ideas box of bricks that have instructions for some things to show the kids what's possible to build (we had the 1500 piece one from Asda last year and it has some lovely ideas in).
And for any adult Lego fans, if you're struggling for ideas for yourself (and already have a velvetiser!) I got the botanical flowers for my birthday this year and they are absolutely beautiful in a vase on the shelf. I also got the aquarium that people are buying and it's fab!