It depends on what you will record (SD, HD ie 2-10+ Mbps streams) and more so on how many simultaneous recordings/playbacks you foresee occurring. Also factor in if you are using a SAT>IP unit, the stream will go from the SAT>IP server -> Tvheadend -> NAS resulting in double network usage for each stream. Same goes for playback: NAS -> Tvheadend -> client.
I record some content to an NFS mount on an old Linux PC and never had any problems, although I doubt I ever went over 25Mbps in total recordings/playbacks at the same time.
As far as TCP vs UDP, I recently had to switch one NFS server from UDP to TCP because I enabled jumbo frames on my network, but my satellite stb does not support jumbo frames and thus could not use UDP. (For TCP it negotiates the correct frame size and works fine.) Anyway, concerned about loss of performance, I did some speed tests between the server and another linux box and found the difference between TCP and UDP to be trivial for NFSV3 and NFSV4 TCP marginally faster than NFSV3 UDP. I found more differences in adjusting rsize, wsize and of course enabling jumbo frames.