Unfortunately, tripods that lend themselves well to birding and big lenses usually don't lend themselves that well to hiking and landscape. Maybe consider planning on eventually ending up with 2 tripods, one for birds and one for landscapes/hiking. Then, to keep costs under control, sacrifice weight and portability on the birding tripod. Logic being you're already carrying a large lens- what is a couple extra pounds of a heavier alloy tripod? Plus, you are more likely to stay close to your car or house when birding than when shooting landscapes, so the need for an ultralight tripod is less. Then, you can get a smaller tripod for hiking/landscape use, and focus on having it be compact and lightweight. Since it won't need to play the role of supporting a long lens for birds, you can get a smaller/lighter tripod that will be all the more portable for landscape work.
From what I hear, the gimbal mounts are where it's at for birding. Theoretically, since shutter speeds for BIF are typically fast, I am not entirely sure how much "stability" you really need, other than enough to hold up the lens. However, I don't bird so I don't really know firsthand. What I might recommend though is looking for something you can grow into, namely a tall tripod. Something like a Gitzo 3-series XLS systematic might work well. Buying used might get you below your budget limit. Going alloy, basalt, or even wood with this may help reduce costs too, because portability may not be as important for this application.
If you're a serious birder, you probably want to eventually pick up a gimbal system that you can mount on it, so plan on it and get the right platform for it now. The Wimberly sidekick ($250) paired with the right ballhead can be quite economical and quite versatile, and gets you into gimbal land without breaking the bank. As you are shooting a relatively "compact" birding lens, the heavy duty setups designed for the bazookas are pretty overkill anyways. The key is that since birds usually have you pointing your lens up, you need the extra height of the "long" or "tall" tripod variants like the Gitzo XLS (you want it to be well above eye height fully extended) so you can track birds while standing straight up.
Anyway, to answer your question, I have a Gitzo 2531, just like Phrasikleia. I use it for hiking and landscapes. Why do I like it? I too like the 3-section over the 4-section because it has 33% fewer leg locks, and is therefore a little faster/easier to manipulate in the field. The CF is lightweight so it's easier to carry when hiking, and it's well designed and well made, so I don't have to think much when using it. It's kind of hard to explain, but not having to think about things like "well if I extend the legs too far it gets wobbly" or "better not put it in the water because it might get damaged" makes using tripods immensely more enjoyable. And the more enjoyable it is to use your tripod, the more you are inclined to actually do so- a key element of the equation. The best tripod in the world is useless if you left it behind because it was too fiddly to use or too heavy to carry with you.
Anyhow just my thoughts
Ruahrc