Install PLEX Media Server on your PC before you do anything - it is free after all.
PLEX will let you stream content from your PC and will transcode it for whatever device you try to play it with.
If you have a SMART TV then you might have a built in PLEX app already and it's possible that DLNA will work better via PLEX's built in DLNA streaming server rather than whatever you're using at the moment.
If you find that you're not happy with how PLEX is performing with your TV's built in capabilities then both the Chromecast and Amazon Fire TV are great choices.
However, I prefer the Amazon Fire TV because:
1) I subscribe to amazon prime (£89 a year) which gives me free next day delivery but also a host of free TV shows and Films (like Netflix) that work great with the Amazon Fire TV.
2) It can be controlled with a remote. The remote it comes with is great but I don't use it because I've paired the Amazon Fire TV with my Harmony Smart Control - something I can't do with the Chromecast
3) I don't have to use my mobile phone to control it. Like the same point above that it "comes with a remote" but in practices this makes it much easier for other people to control it (i.e. my girlfriend).
4) Built in apps for YouTube, BBC iPlayer etc all work without any other device required. Don't have to have a PC on. No need for my phone to have its battery charged. All just work independently of any other device.