Welcome to Android Central! Try going to Settings/Apps/All, and see if you can sort by size (tap the menu button when you're on the screen). Then see if there are any apps that are taking up an inordinate amount of memory. You can then tap on the app to see if a lot of the memory taken up is cache, which can be cleared. Might be worth trying
App Cache Cleaner to see if this can temporarily free up space.
As to your question about the proper way to hold the smartphone--it's totally up to you. As long as you don't have an iPhone 4, any natural way of holding your phone won't affect reception. Most phones can have decreased reception if you hold them with a so-called "death grip" (i.e., holding it tightly and covering a lot of the phone back, typically with 2 hands), but in reality, no one really holds a phone like that. How to hold it while typing depends on the keyboard that you use. If you prefer a keyboard that you tap, then landscape might be easier, so that the keys are bigger and easier to hit with your thumbs. If you prefer a gesture keyboard like Swype or Swiftkey, it's probably easier to hold it in portrait orientation, so there's less distance to cover when dragging your thumb or finger over the keys. For taking pictures or videos, just make sure your finger doesn't block the lens.
Enjoy your phone!