Very good question. I was going to say the PSP but I recall having a free government phone because at the time I had a really poor job and we used to get EBT and back then and probably still now you can get one of those free government smartphone or flip phones and that's what I had.
For the life of me I can't remember it may have been a Motorola but it had a one and a 1.5"~x1.5"~ screen and it would browse in a very funky fashion. Back then a lot of websites probably weren't still optimized for every device and unlike now where we have a little more standards and far more mature mobile support across websites and obviously applications, this place didn't load right at all on that but it was such a convenient thing that I put up with browsing and that limited fashion.
To the same point I remember using either the ESPN app or a web page that was really mobile friendly and I was able to check scores as they happen I recall either having the refresh it or whatever but those were the days.
The true answer as far as being able to competently browse had to be the psp. As much as I love technology and everything else I was really laid to the smartphone and recall not getting one possibly until 2011.