If it were strictly a choice between ubuntu and mint, I'd say just go with mint. Ubuntu can be fun for learning and playing around with a linux system, but it can also be frustrating sometimes if you want to do something a bit more advanced, because the developers have hidden how some things work or made them more difficult to get at than on other systems in their attempts to make it more user friendly. Still, both of them have some good things going for them.
Personally, if you want something relatively noob-friendly, I'd suggest Fedora out of personal preference over Ubuntu. It's what I learned things on, and since pretty much anything you learn on it will be done in a fairly similar way on Red Hat (as far as the basics go, at least), which is one of the more widespread distros you might encounter in a business environment, so it could help you out there.
For overall preferece, I like Arch, but I wouldn't consider it noob friendly unless you've ot a lot of patience and are good at following technical instructions. Even then, sometimes it'll just throw you a curve ball. I got "This should never happen - bailing out" as an error message from the installer once.
I think a decent idea would be to grab an 8GB thumb drive, head over to distrowatch and check out a bunch of distros. If you find one you like, download an iso and make a bootable thumbdrive with it. Then you can test it out without the limitations of a liveCD's sluggishness or formatting your hard drive. Try out a few, and install the one you enjoy most. Everyone's needs are different, so while Arch works best for me, you might find it completely unusable. The good thing is, there are a ton of distros for you to choose from.
Also, on a sidenote, slap whoever told you Mint was minimalist for me. They might have some nice minimalist looking themes, but unless they've changed things since I last installed them (which granted, is possible seeing as it's been about two years), Ubuntu and Mint have a ton of extra crap in them to make them easier to use out of the box for the largest amount of people. If you're looking for something minimalist, look elsewhere. Go upstream a little ways and just get Debian if you want. You can do a nice minimalist install of Debian, but you'll have to get your hands dirty to do it, rather than the nice streamlined installers for Ubunut/Mint, where you pop in the disk, click a few buttons and go have a beer while it sets up everything for you. You could also go with Arch or one of the many BSds for minimalism, though they're not particularly known for being noob-friendly. If you can read
this and it seems like something you could follow as step by step instructions, then that's another option. Thre's plenty of links that will lead you to articles explaining how to set up a lot of basic things. FreeBSD also has some pretty good documentation. I would advise you to steer clear of anything like Gentoo or LFS. LFS has you build everything from the ground up, yourself, which is obviously rather overwhelming (I want to try it, but I'm not sure I could pull it off all the time without getting angry). And while Gentoo doesn't necessarily have to be any more difficult than Arch, if you're not compiling from source for the majority of your packages, you're missng the point of running Gentoo in my opinion. And if you are, it's a much bigger headache for the beginner just trying to learn.
Short version: Don't limit yourself to one version or another right off the bat. There's tons of distros out their with various strengths and weaknesses. So try a bunch and find one that works for you, and slap that person who said Mint was minimalist for me.
Edit: Also, if we're recommending things, it'd be useful to know a little bit about your laptop. The thing that specifically comes to mind is, are you using a BIOS boot or UEFI, and do you use or plan on getting a harddrive for this system that's larger than 2TB? I just spent my entire weekend on another forum about 2 weeks ago helping some guy out becaus he was in the same situation. He went with Ubuntu (I was the only dissenting vote, again pushing Fedora instead) because a ton of people said they liked it. Two days of nearly constant back and forth with him, and then he mentioned that he was trying to install to a UEFI system, and wanted to install to a 3TB drive. I'm pretty sure Ubuntu automagically wil configure everything for a UEFI boot now, but the last time I looked, it absolutely will not work with a drive that's larger than 2TB out of the box. This is because Ubuntu doesn't enable a necessary kernel module in their stock kernel. It's relatively simple to fix it (just compile your own kernel and enable that option, there's plenty of guides online), but it might be quite a bit more work than what you want to do right away. I know Fedora is one of the noob-friendly distros that'll work out of the box with such a system, though. Still, if you gives us some info about the system you plan to install on, like parts and such, we'll be better able to tell you what will and won't work, or warn you about any pitfalls you might encounter. It's a lot better to learn about these things beforehand, rather than realising there was a bug in the drivers fo your networking hardware and that you'll have no internet access after you've already formatted your harddrive.
