PG was easily our worst position last year. Upgrade that position and facilitate the rest of the offense better, and I think this team is special. For me, improving at PG was something that simply had to be done this off season.
I would sign someone like Lin, play him for two years and as Exum grows into his role, give the reigns to Exum. Perhaps they split minutes next year and by year 3 Lin is the backup, nothing more. Meanwhile, you can trade, waive, or just not resign Burke.
That's absolutely what I would do.
Plus, if Exum takes off in a year or two, I think we could easily trade Lin to someone desperate for a PG then like we are now.