Step 1: What helps solvation?
In water, a positive ion is held more firmly when it has more N-H bonds to form hydrogen bonds with the water.
Step 2: Count the N-H bonds.
$\text{R}_3\text{NH}^+$ has one, $\text{R}_2\text{NH}_2^+$ has two, $\text{RNH}_3^+$ has three, and $\text{NH}_4^+$ has four.
Step 3: Choose the best.
With four N-H bonds and no bulky groups in the way, $\text{NH}_4^+$ is held most strongly by water.
\[ \boxed{\text{NH}_4^+} \]