While game updates may contain newer firmwares, they don't require you to update to that firmware to play them. Newly released games function off newer and newer IOS revisions - each game needing a certain set to play off of.
3.4 was originally designed as a homebrew disruptor for the older hacks, pre-bannerbomb if I have my history right. The increased functionality you heard of in 4.x is a compatibility with SDHC cards and the ability to place and load channels on the sd card. Another advantage of 3.2, 4.0, 4.1, 4.2 firmwares is the option to install and use Priiloader, a recommended anti-brick program.
You don't need to update your firmware, it's your choice. If you choose to, and have no online option, you'll need to download and install the trucha signed ios for the sysmenu you want to change to (ios60 for 4.1), the sysmenu wad, and install both in that order.
Edit: I should have also mentioned - if you want to stay on 3.4 make sure your ios' are up to date using NUSD and update IOS 38, 50, 53, & 55.