Using USB Memory Stick for Media Storage

I’ve installed OSMC on a Raspberry Pi Model B Plus Rev 1.2. It has USB WiFi, OSMC remote control USB dongle and HDMI devices attached. Right now it also has a 16 GB USB memory stick. I’d like to upgrade that memory stick to 32 or 64 GB. Will there be issues with either on this setup?

32/64GB stick should be fine.

Not from a OSMC point of view. Just with all that USB devices you want to ensure you get enough power

Yes, I guess power was my initial concern. How can I detail the power requirements of those devices, in particular the OSMC remote USB dongle and the WiFi USB. Also which would be preferred from a power stand point, USB 3 or USB 2 Memory sticks?

Well USB3 surely has higher power usage.
Maybe consider powered USB hub

If your talking a average low cost thumb drive and not something like a usb attached SSD the power consumption should be quite low regardless of size and should only be an issue if the power supply on the RPi is marginal to start with.