I spent a week in Maine this month and the 16-35 f4 was on my camera almost the entire time.
There are numerous wonderful wide angle / uwa primes, but I think if you are budget limited the 16-35 is the way to go.
For the 55 / 85, for autofocus, look into the Sony 55mm f1.8 and 85mm f1.8. I wasn't a fan of the 85 f1.8 personally but most people like it as a cost effective portrait prime. If you want to consider manual focus for the 85 as a landscape prime, I like the c/y mount Zeiss 85 f2.8 -- lightweight, very good image quality.
To save money, consider buying used. fredmiranda.com has an excellent buy/sell board.
Thanks! I was able to pick up a 16-35 f4 used locally (well not yet, picking up tonight) for $825, which seems like a great deal (a few scratches on the barrel but doesn't look like anything crazy).
Most of my shots are on the wider end, I only wanted to go with a 50mm or 85mm for the occasional times where I feel I need more reach (shooting down a street, a portrait, something that just needs more reach vs 35mm, etc. The 55mm is just a bit too expensive for a lens that will be secondary.
The Sigma 24-105 f4 Art w/adapter seems like a decent choice if I can find one used for a good price. I'll have to read up on how well the adapter works (I remember some issues when I was considering Sony a few years ago, but that's likely changed I'm guessing).