Should I patent the new novel mobile app fully or should I patent the methods?
This is a false dichotomy: you should patent the invention (or inventions), regardless of how it might be implemented.
To determine what the invention is, you need to determine whether the different components can usefully stand alone.
For example, each algorithm might be pointless on its own, and simply involve shuffling data around. If so, these algorithms are not really inventions. In this case, the invention might therefore be a method involving the use of both algorithms together in the context of a mobile app.
On the other hand, one of your algorithms might be a unique way of error checking data transmitted across a network that is faster than conventional methods. This would be useful in many situations (even though you only intend to use it in your mobile app). The invention (or one of the inventions) would therefore be this algorithm alone.
By focusing on what the invention is (rather than what your product is) you will be maximising the scope of any resultant patent (and thus the protection that you obtain).
But it must be patent-eligible
In the US per Alice v CLS the subject matter of a patent claim may not be directed to an abstract idea. An algorithm may be an abstract idea. However, since Alice-style abstractness is quite beyond the scope of your question, I simply flag it as a potential issue (and would invite you to ask a further question, should you feel it necessary).