OK, so you look like you are not to fazed by the concept of messing around with partitions. Here is what I would do.
Use the windows tool to shrink down the windows partition to what ever size you want to have. I believe it is then a good idea to start windows a couple of times to let it decide it is happy and to run ckdisk if it wants to, and that de-fragmenting before you start is to be recommended.
I would leave the rest of the space empty. The windows tool can't format the free space into the type of file system you need for a linux install
Start the installer and choose the option "something else" (at least I think that is what it is called. The one that lets you do the partitioning manually.)
I like to make a separate partition for my /home folder. Doing that allows you to simply re-mount that partition if you need to do a fresh install for any reason. That is where your data and your config files are stored. Being able to re-mount that has saved me some bother a few times.
So, make an extended partition using up all of the free space. Linux can be installed in a logical partition without a problem. (I hope no-one comes along and contradicts me on that...)
Inside that, make a partition of around 15GB and choose / as the mount point. This is the partition that the system goes in to. You can give it a bit more space if you have plenty of room on your drive, but, say, 50GB would be overdoing it. You can see from the attached screenshot that the /partition on this machine is just under 12GB and only has a bit less than 4GB in it.
With the rest of the space, you need to make a swap partition and one for /home. I always put the swap at the end so that I don't have to move it if I want to change the partition set up at a later date, but that is just me.
If you want your standby function to work, you should give the swap partition a little more that you have RAM. When the computer goes to standy, the contents of RAM are written into the swap space. If you never use standby, about a GB of swap should be more than enough unless you do things like really intensive video editing, or having hundreds of photos open at once.
The rest of the space becomes one partition that is mounted at /home.
I hope that is clear enough. If it seems confusing, go into the installer and have a look at it. The installer doesn't do anything permanent without telling you it is about to do that. You do have a chance to bail out if it all gets too confusing. Just look carefully at what you are seeing on the screen.
Doing a backup of anything important in the windows install is a very good idea before you start doing any of this stuff. The installer is quite ok, but you never know. A power failure, for instance, half way through the process could be bad news.