Solder Iron/Station Advice

My current 25W iron from Radio Shack which is more than ten years old and has a tip that seems to be bulky to solder a male header to a LCD. I haven't even tried to solder the header yet to the LCD yet because of this.

I'm thinking of getting a new solder station 5W to 40W (Jameco #146595) for $49.95. Or a 40W Soldering Iron (Jameco #2094160) for $24.95.

Anyone have any thoughts/suggestions on the new iron/station or get a new tip (bulky) for the 25W iron that I already have?

Thanks in advance.

I use weller... and this tip https://uk.farnell.com/weller/s/tip-conical-long-0-4mm/dp/836242 This tip really needs a temperature control to keep the tip in good condition though. So if you can afford it go for the adjustable one

https://www.youtube.com/watch?v=R_PbjbRaO2E&feature=player_embedded#at=510

Segment from Dave's EEVblog about how to set up an electronics lab.