If you are travelling around, I recommend you get one with Intel
Centrino Mobile Technology.
Simply putting, it will be Intel Pentium M xGHz. x is a decimal,
like in your question, 1.8GHz. Depending on what games you want to
play, you may not want a Intel processor. A AMD Sempron processor
works as well.
To answer question 1, you can add RAM. If you are unsure, you can
ask the sales technicians to help out. Or simply take the upgrade
offers (like Dell, offer you upgrade this, upgrade that).
For question 2, all laptops have at least one USB port. Just buy a
mouse that uses USB port and connect can already. Nowadays laptops
don't come with PS/2 Serial Port, so make sure you don't buy the
wrong one, or you have to use the black space (it is called
touchpad).
Question 3: I won't recommend brands, but laptops that are using
Intel processors have longer battery life.
Question 4: If the hotel has wireless infrastructure, just register
with the hotel to use their wireless network. If it doesn't have,
it usually have some ports for you to connect to the Internet.
Check with the hotel, you can email the hotel or ask around, like
your friends who have been to the hotel.
Yahoo is a good site to find old and in good conditions
laptop.
If you want to play games like RPG, I recommend you to get a
desktop replacement. Their processors are usually Intel with HT
Technology or Intel Celeron or Intel Celeron D.
