I'm new to the wiring/electronics part of arduino,
So you will find that the MAX6675 is quite good value for money. You need to amplify the signal using operational amplifiers. With such a low voltage signal these need to be very good operational amplifiers. They have to be carefully designed and even more carefully constructed. No doubt other might suggest a circuit but my advice is that it is a lot quicker, and cheaper and you get better results using the MAX6675.