Glad to see you all answered and gave your views for my question. I have downloaded Elektrum for android as you recommend. I haven't bought anything for me to keep in my Electrum wallet. The next step may be the security of the wallet I use. I got a good current source of reading from the official bitcoin.org site. Thank you very much.
Just remember, that if you are using that android phone as a regular device, and downloading apps from the app store you should be wary of storing any wallet on that device. Many apps on the app store have ridiculous permissions that they require, and Google can't verify that every single app isn't malicious. So, with the correct amount of permissions, and a malicious piece of code your wallet could be susceptible to an attack. The risk is the same on a computer, except for people are more likely to download unknown apps on their phones, because in modern times phones are used as a primary device.
Its preferred to have a dedicated device to host your wallet, and if you don't require regular access, then a offline wallet might be the better option. If you require regular access, then you might want to consider a hardware wallet. Despite the cost, they do have some extra security protocols which help with the less technically minded.
