This summer, we bought a $20 booster high chair at Walmart for travel and our baby prefers it to any other high chair she's sat in. So I would recommend it for its very small size and great functionality. It's called the Safety 1st Easy Care Swing Tray Booster. We've used it since the baby could sit up and she's now 15 months and still loves it, with room to grow.
For a "real" chair, I love our Bjorn high chair, and our older used it until age 3.5. He's skinny and tall, for what it's worth. The little one uses that one too, but as I said, prefers the Safety 1st one.
We also had the Ingelsina one that attaches to a table, which our oldest really liked. It goes up to 40 lbs if I recall correctly.