You need any kind of mobo/CPU combo, I've heard 12th Gen Intel onwards are as capable of transcoding on the fly as an older GPU so you wouldn't need both, but if you go older I recommend a GPU as well, just because it gives more flexibility with being able to use hardcoded subtitles without locking up the CPU, and streaming a lower bitrate version of the video if your internet is shit, instead of - again - locking up

For easy certificate management I use NginX Proxy Manager, for media I use Emby and for a domain I use Cloudflare but you can absolutely serve your server with DuckDNS or another DDNS service for free.

I paid about £200 to build my server, with a £30 CPU (Intel i6 3100), free motherboard, £50 PSU and £110 SFF case (rough costs), and holy fuck it's so much cheaper than any subscription. Electricity is about £3-£5 a year and other costs are optional. I also sourced a GTX 970 for £90 that was more than up to the task of transcoding, but again, if you get a 12th gen you won't need it.

I just remembered the HDD I started with was a spare (10TB Seagate Barracuda Pro, but I shucked (like shucking for pearls) an external HDD to get it, as I heard that you can get lucky and get a good drive for cheaper than it would cost to buy it. Said eHDD was about £250.