London And/To SouthHampton suggestions

Good morning, Planning our trip and have a couple of questions and ask that you be kind as i'm a detailed oriented person.
We will be flying into London in March from Atlanta, the morning/day before our cruise. We have traveled several times to Europe so are familiar with our travel habits. Reviewing our 2 options first would be to transfer to South Hampton after the flight before we get tired, or the one i wish to do, is to stay the day in London, hit a few sights since this is our first time in London. Then take a train to South Hampton the next morning after having breakfast in London. We usually crash around 8pm the first night and then are up before sunrise and feeling great the next morning. Is there any valid reason for not doing that.
If this is reasonable and doable then i have a couple of questions.

a. are the trains between London and South Hampton always reliable.
b. where would be the best area to stay in London to make the train easier, more direct, the morning we transfer to South Hampton.
c. What is needed to get between the train station and the MSC cruise port in South Hampton.

Thank you for any advice and experience that you have to share.
 
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