First Linked List in Java
Disclaimer: This review is reviewing this as work-in-process, and not as "finished".


On a quick glance this looks mostly correct. I still got a few points, that definitely need to be fixed before proceeding:


Index handling:
You don't do anything with negative indexes. vector.getAt(-1); results in an infinite loop, as well as vector.deleteAt(-1);. I suggest you just check and throw an InvalidArgumentException for any \$index &lt; 0\$ 
Empty list:
Your empty list throws null-pointer exceptions all around. Don't do that. You should check your head before doing stuff with it, and if it's null, throw IllegalStateException  or similar. 
Optimizing pushBack():
There is a relatively simple and quick-to-implement optimization for your pushBack. Your Vect&lt;T&gt; should maintain a "pointer" to the last node. On deleting the last node you need to check for the special-case just like when deleting head, but after that your pushBack becomes dead-simple:

 public void pushBack(T cargo) {
     tail.add(cargo);
     tail = tail.getNext();
     vSize++;
 }