Does your iPad1 have cellular access (as well as WiFi)? Because, if you are using the cellular access the access the AppStore, you will get a notice to use WiFi (or iTunes) if the app you are trying to download is over 50mb in size. It's a restriction built in to save bandwidth. If this happens, you acres WiFi on your iPad and then re-try the download again; on WiFi there are no restrictions.
For the AppStore sending you back to the home screen unexpectedly, that's called a "crash." The iPad will do that sometimes, especially on the iPad1. There's no harm being done - its just your iPad's signal that it's run out of RAM. When this happens, close out all other apps, including the AppStore one (via the multi-task bar) and then re-launch the store; it should work. Just one of the limitations of "only" having 256K of RAM...
Hope this helped.
Marilyn