Excelsior Hotel mall near Funan Mall seems to be one of the best place to find guitar stuff. It's a little bit shabby, but basement and 1st floor have good stores. I just started to learn to play the guitar 2 months ago: learning with a teacher really helps... I tried alone but i was going nowhere.
I can give you the ref of my guitar if you want (it's a Yamaha), my teacher says he really like it, and want to recommend this model to his new students (actually he wants to buy one too

)
To tune a guitar, just buy a tuner

It cost like 10/15SGD, make sure you get the kind that you'll clip on the head of the guitar. Then check on youtube, there's probably a video of someone demonstrating how to tune a guitar. (would be easier to understand than if i tried to explain with words)