Why is that a problem? A 'good' NAS is a much more elegant solution vs. handling the transcoding externally. Decent NAS setups with good-enough CPU performance are getting a lot easier, and cheaper, to find now. If you transcode correctly and setup your Plex configurations right, subs and audio formats are not an issue.
My BT-based NAS + Plex definitely passes the 'wife test' at home. It's simple and all you need is a Plex app on the device(s). IMHO, the Chromecast is just a stop-gap solution for deficiencies in existing hardware.
In any event, the OP has what he has needs to get this to work. I would agree that a Chromecast + XBMC would be the best option for not a lot of $$$, but not ideal.
I'm caught in the middle here. Sickbeast's suggestion desreves scrutiny, but only because his improvised solution has a lot of potential to cause frustration. It might be a nice stop-gap solution but a laptop as a Plex server? Please..... You need to build a NAS/Server with the idea that it is always on and ready to perform its duties at any time. There may be down time for specific services to perform maintenance but the moment you start planning to turn on the server so you can do something on the client side makes a server rather pointless. You might as well just hook up an external HDD or two and just turn on your PC when you want to watch something.
Poofy is right when he says that transcoding introduces a whole lot of issues that can be avoided by spending the right amount of $$$ on the client side. Transcoding should be viewed as a convenient backup when the file won't play directly on a random client but shouldn't be relied upon to be your prime time player if you can help it. Plex has done a nice job with making plugins available for various clients and they do a nice job in keeping it as headache free as possible but like he said, you just can't account for every variable in your streams. In addition, anytime you transcode, the image is degraded. Why pay for a Blu-Ray when you are just going to crush your shadows and add artifacts by transcoding? You might as well just get a NetFlix account.
But to be a devil's advocate, there are some very solid reasons in going with a higher powered server and a service like Plex. I use Mezzmo instead of Plex but the concept is the same. I use it so that I have a consistent experience on any device that comes into my home and wants to consume media. If someone sits down to a TV or picks up a tablet/cell phone they can just jump into XBMC, Mezzmo Mobile App, their TV's menu or whatever and when they find "BrettFlix", they get the same library and organization every time, regardless of the client. I can also control what media is available at different locations and set up parental controls according to who is watching so that Mom and Dad's movies aren't even available in the 9 year old's room.
I can also bring any other device into the home and Mezzmo will automatically take a guess as to what it will take to make sure that media will stream smoothly to it. If a relative comes in from out of town and wants to watch a movie on their tablet, they can just load up the DLNA client software and pick something out.
Tinkering with device profiles is a neverending battle, though. I am now on the tail end of customizing a device profile for my Raspberry Pi that runs XBMC. It kept insisting on remuxing and/or transcoding all of my BD Rips even though their codecs and streams were 100% playable without transcoding. Took multiple e-mails to Mezzmo support and over a week to figure out that the embedded PGS subtitles were being logged as unsupported and Mezzmo wanted to Remux to make them compliant. I never had this issue with my Chromebox running XBMC because it can handle just about anything so I can just shut the transcoding off completely. Plex or not, there is something to be said for a trouble-free client. That's not too mention the time spent tweaking profiles for the Kindle Fire, my Blackberry Z10, Nexus 4, Tabeo, DirecTV boxes, and the apps that are used to play back the files. There is literally nothing I hate more than not being able to do things like FF/Rew while I wait for the file to be transcoded for a device that doesn't need it.
There's just two schools of thought here.
Theater buffs are gonna lean Poofy and wanna just be able to pick up a shared network file and play it back smoothly on a powerful client. They probably have a MySQL database that all of their HTPCs pull from and a stack of DVDs and BDs in the garage that they spent days ripping to their Atom-Powered server that they crafted from a Norco Rackmount case and some parts in their garage. Budgets are bigger and the set up is more detailed.
Many other people just want to be able to pick up their phone, or their friend's phone or their sister's tablet, or the remote control to their living room BD player and pull a downloaded video file off the PC downstairs. They don't peek at pixels and don't get annoyed with the judder created by 3:2 pulldown or the blocking in the background because the compression was too high. Heck, my wife still doesn't care if she's watching SD or HD.
Still, though, a good NAS is the foundation. Know what you want going in.