Apologies if this is obvious: The smaller the Kelvin temperature, the warmer (more yellow) the light. If you are trying to make them blend with other incandescent lights, you want to be in the 2500-3000K range. AS you get up around 4000K it is often called "cool" white, and you can choose that if you want it to stand out in the midst of regular incandescent lights; these "cooler" (higher number) colors tend to look brighter even if they are not. If you want something close to daylight, you need about 5000-6500 (higher looks bluer and brighter).
LED tubes come in a huge variety of color temperatures and "whiteness". Most are not very white, and make colors look a bit funny, but we are all used to it and do not notice much, but if you want more accurate color pay a bit more and get a better one.
However, as mentioned above, you may want to consider replacing with LED's. They make LED replacement "tubes" for florescent fixtures that offer some serious advantages - less power usage, less heat generated, better color, and (if you are careful in what you get) they may be dimmable.
These come in two varieties, those that just fit in place with no wiring change (i.e. "requires ballast") and those that expect you to remove the ballast. The latter are better in some ways -- one less thing to fail, a bit less energy usage (not much different) and easier to get dimmable ones -- but it requires some minor rewiring. Easy if you are at all handy. I recommend this approach if you (or a friend) are comfortable removing the ballast and twisting a few wires. This also removes some buzzing and humming that can occur with ballasts.
I've seen, but never tried, some that are supposed to work both ways (with and without ballast).
If you want dimmable, buy carefully, as most are not.
Some may have "CRI" ratings. The closer to 100 the more natural colors look with them. Probably anything over 70 or 80 is better than most florescents (depends on the florescent of course). Unfortunately most tube replacements do not seem to be rated.
I've replaced almost every florescent fixture in our house -- think maybe 1 left. Much brighter usually and never need to touch them again (probably).