You have a fundamental misunderstanding of naval invasions.
First, all new players need to get a few concepts well under their control in order to successfully conduct naval invasions. You need the proper transports available, all the way from the launching port of the invasion to the intended invasion area. You do not park ground units off-shore before an invasion, that actually works against you (from my experience). When you look at your transports you see two numbers like this: 25/2. The first number is the normal transport points and the second is amphibious invasion points. Keep in mind that a normal infanrty unit requires 4 points of transport to move on the sea (for each area). In the example of 25/2, you could move 6 infantry units across the water in non-invasion movment (6 x 4 = 24).
You are always going to have to pay that transport cost whether we are talking about strategic movt or invasions. The difference with amphibious invasions in that the second number is used in the amphibious invasion area. At the amphibious invasion site you are going to need alot more transports. In the previous example of 6 infantry units, you will need the 24 regular movt for each area you pass through to the invasion area PLUS at the invasion area you will need 12 transport units (24 / 2 = 12). Also, make sure your line of transports is unbroken from point to point and that at each point you have enough transports to handle regular movement. For example, moving 8 infantry units requires 2 transports for regular movement through each area (that uses 36 of the 48 points).
Amphibious initiative: In my experience you will want an army commander to provide amphib initiative for the general you plan to conduct the invasion with at the point of embarkation. Once your commander has amphib initiative and enough transport exists from point to point, just send him in. Relying on an individual commander to gain initiative without the help of an AC is a hit or miss proposition. If your AC is out in the field, conducting amphib invasions is going to be tough.