Let me just point out a few things. As I said in one of those posts that I referred you to, partitioning a Linux system is a very contentious issue. Everybody seems to have strong feelings about his or her own way. I am not about to get into a discussion about what is the "right" way to partition. I'll just give you my thoughts and you decide what you want to do.
I am going to assume that you are after a general purpose desktop system and won't be doing a lot of program development, or compiling a lot of your programs. If that is the case then the rest of this post applies to you.
I'll use a Kubuntu system, which is similar to Mint, I have on my computer as an example. I set it up as a general purpose desktop. I use a swap partition, a /boot partition, a / (root) partition, and a /home partition. To be honest, I could do without the /boot partition, but since I have a number of systems on my machine I use a /boot partition for each OS so I can keep them close to the top of the partition tables. The closer a file is to the outside of the disk the faster it can be read from. The kernel is in the /boot folder.
The size of my Kubuntu / (root) partition is 12 Gig. Believe me I have a lot of extra stuff added in for testing etc. and am still only using 6.2 Gig of that space. I can't imagine how I could possibly run out of space in / (root) using it as an average desktop user would.
You have /var sized at 15 Gig. My var is currently using 350 MB. You have /user sized at 15 Gig. My /user is using 4.1 Gig., the largest file in / (root). My point is that every partition you make you have to size for worst case. You therefore tend to allocate too much space and it is just wasted. If you go too small you might run out of room and break the system. If you leave those files in / (root) they can expand or contract as needed without having to allocate so much space to those files alone. There are other reasons why I do as I do but I think I made my point.
In your case you only have one disk installed and Windows always needs to go on the first partition of the first hard drive. This is the Windows way. Windows kinda works ok if done Microsoft's way. It hardly works at all if you don't play by their rules. If it isn't on a primary partition on the first partition you will have ongoing problems with installing some programs and strange things happening in the registry. You can make it work but the problems will be never ending, according to those that know a lot more about Windows than I do. Below is what I would suggest in your case. If you choose to do otherwise thats fine. It certainly won't hurt my feelings. This is just my recommendation, for whatever it is worth.
sda1 primary see notes ntfs Windows
sda2 primary swap see notes swap Linux
sda3 primary / (root) 10 Gig ext3 Mint
sda4 extended /home rest of drive? ext3 Mint
sda5 logical shared see notes ntfsNotes:
1) You need to size the Windows partition for as big as you think Windows, programs, and data will grow plus at least 20%. 2) The swap partition should be twice the amount of ram you have but the total should not exceed 4 Gig. 3) If you have a lot of space to work with it is handy to have a shared drive that both operating systems can use.
Hope that helps.