I once had a cheap umbrella stroller - it was a complete waste of money. I upgraded to an umbrella size stroller with more features. The one I have is made by Chicco similar to this
http://www.chiccousa.com/gear/strollers/liteway/liteway-juniper.aspx. It has a good sun shade, basket, reclining seat (my girls slept many hours in it). I have taken that stroller to many places over the past 8 years (many zoo trips, Sea World, San Diego Safari Park) and it is still going strong. It is easy to handle in airports as well. When my girls were little, I got a double stroller from Chicco that was basically 2 of the single strollers put together (1 center handle). It worked great too and went a lot of places. I still use the single stroller going to zoos to carry the small ice chest and other stuff, but the girls walk.
I had a Baby Trend Sit n stroll and it was merely ok. It served the purpose, but it wasn't great. The description above of pushing a sled is reminiscent of it.
The big thing to be aware of are the weight limits in strollers. Many are 35 pounds and if you go over that they are impossible to push.