Yes, I followed the normal main quest line. All mods seem behave ok.
After digging hard on the internet I found there are some people having the same problem - "No option to buy Breezehome and Lydia is using throw voice lines". But no one knows what causes it and how to fix it.
The issue persist even I deactivated all the mods and reloaded the save, seems like the damage has been done to all the saves.
My suspicion is on mods that alter quests may have conflict with another mod - Alternate Start; The Choice is yours etc.
I have the same issues Skywalker. No dialogue option from Proventus Avenicci to buy Breezehome, and Lydia insults me when I first speak to her...the nerve LOL. Yes, she is somehow bugged with the Throw Voice dragon shout.
I'm going to say we can rule out Alternate Start because I didn't install that mod in my build, and have stripped it out of the Conflict Resolution plugin so it's not a required master. My game was started without Alternate Start ever being a part of any game save. I can't speak for The Choice is Yours, as that mod is in my game.
I just started noticing these issues yesterday for the first time, and started Googling for a resolution. I've seen reported posts for the issue from back in 2012, and many point to a connection between the missing Breezehome dialoge with Proventus and Lydia not being able to display her dialogue as housecarl.
Time to dig into the issue some more.