All of the currently available Roku devices have the same ARM Cortex A53 quad-core CPU running at @ 1.2 GHz, so there should be no discernible difference between them regarding the speed of navigating through menus or general performance as far as the CPU is concerned.
Some models do have more RAM than others. For example, the Stick+ and Ultra have 1 GB of RAM, whereas both Express models and the regular Stick only have 512 MB of RAM. I haven't seen an officially published spec for the new Premiere and Premiere+, but it's probably safe to assume they are also 512 MB since they're based on the Express model (essentially an Express with 4K added), and they're at the same price point as the regular Stick. (Edited to clarify: The Premiere and Premiere+ might also have 1 GB since they are 4K devices)
Another factor to consider is the NVM (flash) storage space for channels. The Stick+ and Ultra both feature 512 MB of storage space, whereas the rest of the models only have 256 MB of storage with no way to increase it (i.e. no microSD slot). If you only have one or two dozen channels, this probably won't be a big deal, but once you start adding a lot of channels, having insufficient storage space means it takes longer to load the channels.
A lesser factor when considering is the resolution of the Roku UI (User Interface or home page), which I believe is only 720p on the Express and regular Stick models, but full 1080p on the Stick+ and Ultra. I will assume that the Premiere and Premiere+ also have the 1080p UI, since they are 4K capable. There honestly is a bit of a difference between the 720p and 1080p home screens, with the 1080p looking more polished.
Take into consideration your WiFi situation. If you have good 5 GHz WiFi available, then you should consider the Stick, Stick+, or Ultra, which are the only three devices that have dual-band 802.11ac WiFi capability. The Express and Premiere models only have 2.4 GHz 802.11b/g/n capability. That means they'll be forced to operate in the more crowded 2.4 GHz band, which may come into play depending on how many devices you and your neighbors have on the 2.4 GHz band.
And finally, the remote control should be considered. Both Express models as well as the Premiere come with the basic infrared remote, which must be pointed directly at the Roku to work, and lacks all other enhanced features of the better remotes. The Premiere+, Stick, and Stick+ come with the voice remote that features voice search, TV volume, and TV on/off controls. That remote uses WiFi Direct, so no line of site is necessary to operate the Roku. The Ultra comes with the enhanced remote, which is similar to the voice remote but also features private listening headphone jack, with a pair of JBL headphones included.
Frankly, for your main TV, I wouldn't bother with anything less than the Stick+. Yes, it's the second most expensive device at $60, but it's a worthwhile upgrade and investment to gain double the RAM of the cheaper devices, more NVM storage space for channels, the 1080p Roku UI, dual-band WiFi, and the more capable remote.