Yes all the components listed will work. Just make sure the memory you get is rated at 1.35V and NOT 1.50V.
The SSD drives will both fit. The mSata one will fit on the top of the motherboard, directly on top of where the WiFi card will be installed, and the NUC case has a little spongy thermal pad that will press against the mSata drive to dissipate any heat from it. Do NOT remove this from the NUC case thinking it's just some protective packaging material, as it's critical. The larger 2.5 SSD will fit in the lower part of the NUC case, in a little metal cage.
Yes you will need a mini-HDMI to HDMI cable to attach your monitor to it. A VESA mount is included with the NUC to allow you to mount it behind a monitor, but not sure your monitor has the necessary holes for this (not familiar with the Philips model you mention)
Don't forget that you will need a USB DVD-Rom drive to install the OS from, unless you have an OS on a bootable USB stick. An MCE remote control is a great addition to the set-up, should you intend to use it as an HTPC.
Good luck with the build!
Everything should fit. I did a similar build with a 500GB Samsung 840 EVO 2.5in drive (no msata). I used Kingston RAM (KVR16LS11/8) in mine and it works. You can also use a mini displayport to HDMI cable (it supports audio and video, same as HDMI). I shot some videos of my build. Ultimate Intel NUC Build - YouTube You can see the inside of the machine in the second video. The mSATA would install over the WiFi module. I also installed Ubuntu Linux as opposed to Windows. If you have any problems, make sure to upgrade the BIOS firmware on the NUC. If you decide to build it, please share your results. Good luck!