So, I finally got my client to start generating and after I got my laptop optimized for the task and waited over night. My first transaction completed resulting in +50 Coins. Yay!!
Congratulations and welcome to the forum
However, once that transaction was complete, a new transaction hasn't started. Or maybe it has. There's only one transaction in the list but I'm up to 131 Blocks under "Status". Is this the way it's supposed to happen? Does it keep processing on the same transaction and generating coins every 120 blocks or so? Or is it supposed to start a new transaction?
The number of blocks of a transaction is the amount of new blocks that have been generated by the whole network after the transaction. Each new block in the chain means new coins to its creator. One "generated" -transaction in your transaction list means that you have generated one block. You're not the first one to find the concept of a "block" a bit confusing on the first sight.
EDIT: I decided to stop playing around and I set BitCoin up on my high powered gaming rig, forwarded 8333 to it, and started generating on it instead of my laptop. So then I transferred my previous 50 coins to that client but it's been an hour and nothing has shown up for me to accept the transfer.
There's no confirmation of incoming transactions when someone sends to your Bitcoin address, all transactions are automatically completed. Did the transaction show up in the transaction list?
Both computers are on the same wireless LAN. I sent it to just the BitCoin address because I wasn't sure if I was supposed to send to my internal or external IP. I assume external because the transaction needs to be verified by other nodes. Right?
Other nodes aren't going to know which IP you're sending to, your client just connects directly to it. Both IP's are fine as long as the connection routes to the right computer. Anyway, I'd use the inner address inside a network for simplicity.