I highly recommend HDHomeRun EXTEND. It transcodes to MP4 so the Roku's hardware can handle it.
Building a system will end up costing a lot more and won't necessarily be better. I mean, just the tuner card alone costs the price of the EXTEND and it doesn't transcode. That requires lots of cores, Intel QuickSync (probably one stream), NVENC (two streams only), or AMF (Windows only, wouldn't try more than two streams). EXTEND is an ASIC solution.
If you want to record........I'm using Emby on my server which works well enough but I'd seriously consider/try HomeRun DVR. Long term, Emby is cheaper because $100 for lifetime and $25/year from Schedules Direct for guide info. Emby...just...struggles with live TV...even on beefy hardware.
If you do EXTEND, an Atom can seriously handle the Emby Server software with a large HDD for recordings. Also if you do EXTEND, you'll have to use the "mobile" profile (because Rokus are weak) which is about 500 MB/hour. SHIELD and Xbox One S can handle "heavy" which is typically 1 GB/hr.
I have:
3 x HDHomeRun EXTEND (all are set to heavy transcode profile)
1 x Xeon 1230V3 (Ivy Bridge) with 1 x 8 GiB DDR3, 1 x Seagate Barracuda 3TB 7200 RPM for recordings, 2 x SK Hynix 250 GB SSDs RAID1 for OS + apps (including Emby transcoding) running Emby Server on Windows Server 2012 R2
1 x Xbox One S
2 x NVIDIA SHIELD TV
Network is fully gigabit.
There's two computers (R9 390 and R7 360), one surface (Tegra like the SHIELDs), and one phone that can playback everything as well.
Recommend Xbox One S over SHIELD. It costs only a little more ($225 versus $200 and that included a game), has godly amounts of more power, can play BluRays, has fewer issues with Emby overall, and you don't have to pay an extra $100 for IR remote support (Pro version, really got boned on that). On top of that, Xbox can be turned fully off where SHIELDs can only go to sleep.
All devices have Emby + HDHomeRun apps installed. HDHomeRun is used for Live TV when Emby gets problematical.
If you don't transcode, ATSC broadcasts MPEG2 which is more or less the same tech that is burned on DVDs. The problem with MPEG2 is that most devices are incapable of hardware decoding it without paying for a license to do it on GPU. MPEG2 is an extremely heavy handed encoding intended to be high quality and recover from damage. It is not meant to be light on hardware like MPEG4 is.
