Re pruning: I probably should have linked directly to this:
https://github.com/bitcoin/bitcoin/pull/4701I should have mentioned that I actually never have done this particular scenario
Anyway, some pointers:
Re IP: Your laptop will have an IP on your internal network. That is its private IP. Probably starts with 192.etc. If you want to connect to it from outside your internal network, I recommend you fix the laptops' private network IP in the router. (Look for a setting called "DHCP static IP" or similar). Your external (public) IP may change from time to time (depends on your Internet provider). Unless your Internet provider gives you a static IP. Ask them. If it's dynamic you will need a service like NoIP.com (there are others), to make your dynamic IP available at the same connection point at all times. You can find your external IP by browsing to websites like whatismyip.com .
Now, for communication from outside your network to a certain port, you will need to open that in your router config. Also, any firewalls you may have installed on the laptop need to open that port. You may remember it from how you did it when you opened port 8333 for your node? For RPC standard is 8332, but you can (and probably should) change it to another port. Makes it a bit harder for people trying to get "in", if they happen to learn your IPs.
Re config file: Yes, I meant the bitcoin.conf file. There are more options for security like password, ssl certs, restrict to certain IP (the one of your VPS) etc. Have a look here:
https://en.bitcoin.it/wiki/Running_bitcoind#Command-line_arguments All these commands (except -conf) can be included in the conf file.
Re TCP/UDP (from the above wiki article):
# Listen for RPC connections on this TCP port:
#rpcport=8332
From my experience things like that may need a bit of tinkering, so you might want to try this with a dummy system first.