It is the sort of thing where you either need to build it and measure the performance, or get into some very expensive simulation games.
My experience is that reclockers are always a good idea behind a connector, almost irrespective of board material because the connectors tend to be 'interesting' from a RF perspective.
How many layers are you using, and what does the stackup look like?
The ethernet is pretty much easy here, it is after all specified to work over 100M of cable, which makes a competently designed set of pairs on a board look harmless in comparison, is is also (assuming 1 Gig) only 125MHz DDR on all pairs, so meh.
The video ports are the ones that would worry me, because those barely work properly on a good day, and are screamingly fast, and a reclocking driver here would not hurt anything.
The USB3 pairs are another one to watch, but note that many so called USB3 ports actually only connect the USB2 pair, which is comparatively slow (480Mb/s), note that there are traps here in terms of getting good EMC performance because USB is neither fish nor fowl when it comes to the question of single ended Vs differential signalling and there is some very dubious advice floating around as to how to connect the grounds at the connectors.
The quick stuff (video, USB3 data, and maybe the sata) should probably use SMT connectors (with tabs to make them less likely to get pulled off) to avoid the need for back drilling or other suchlike nonsense, but that (and the question of what material to use for the layers in question) very much depends on either measurement of simulation (Very expensive software involved here).
Given the low cost of spinning an FR4 prototype I would probably do that and measure the resulting eye for each signal, it is not like you are especially likely to get it all perfect on the first shot even if you use expensive substrates.
You will very obviously need a ground plane, and it feels like at LEAST 4 layers to get the plane close enough to the signal layers to make the impedances work at sane trace widths.
Final question : Where are the mounting holes? Do NOT rely on connectors to mount this.