Asking what is the best modchip for you is a very open ended question. There are tons of opinions about what is the better chip, but without even knowing what version you PS2 I dont think anyone could give you the definitive answer. I'd say to look at either the Messiah 2 or the DMS chip. As far as soldering goes, all the supplies you need( solder iron, solder, flux) can be got at radioshack. Pricing is going to vary based on quality of course.
Not sure if you have any solder experience at all but you want to make sure you get a very fine tip soldering iron.
NTSC U/C 30001 V.4 Messiah 2