Oh, I read "podcasts" instead of "apps" there.
You just need to be signed into a Google account to access the play store, it's unrelated to gmail. (Other than needing to be signed into a Google account to access gmail too.)
Getting apps on an Android device should be pretty simple, you can do through the cloud with the play store or just copy the *.apk files from whatever source by whatever method you want. Play Store is probably easier and gets you updates, main use of apk files is piracy or apps that Google has banned. (adblock)
I've never found browsing the marketplace on Android to be particularly burdensome (assuming v4.0+, otherwise any action is burdensome), and it's not like it's a particularly regular activity once you're set up with the apps you use.