high chair

My general advice is to (1) be aware of the footprint and avoid something huge and (2) get a high chair that isn't made of fabric, since high chairs get really dirty and you want something that you can wipe clean.

The Stokke Steps System has been great for us because it adjusts to work from infancy through the toddler years (particularly if you purchase the attachable bouncer seat, which can also be used separately, as shown below). The Stokke Tripp Trapp is another great option that grows with your child, and it's a classic design that has been around since the early '70s. I find the Stokke high chairs cuter than a lot of the other options on the market, or at least more neutral and in tune with the style of our home. Many parents swear by the Ikea Antilop Highchair, and the price point ($20) is hard to beat. The Antilop legs actually pop off, so it's really easy to transport. In the space-saving category, hook on chairs (like this one by Chicco) are great as long as you have a sturdy table. 

Lastly, don't be fooled by the Micuna Ovo High Chair, which is beautiful and all over the the interwebs -- the tray is to the side and it's a recipe for depressing, side-slumped baby posture.