I'm not a cabling expert, but solid core sounds weird. Ethernet typically uses twisted pair. Early Ethernet used coaxial, and some exotic Ethernet uses fiber optic. So I'm not sure what a solid core Ethernet cable is supposed to be, unless it's a legacy coaxial cable.
Anyway, the first thing I'd worry about is maximum cable length. Different categories of ethernet cabling have different maximum lengths at different speeds.
This ought to help:
"The Category 6 specification improves upon the Category 5e specification by extending frequency response and further reducing crosstalk. The improved performance of Cat 6 provides 250 MHz bandwidth and supports 10GBASE-T (10-Gigabit Ethernet) for distances up to 55 meters.[10] Category 6A cable provides 500 MHz bandwidth and supports 10GBASE-T for distances up to 100 meters. Both variants are backwards compatible with Category 5 and 5e cables."
So if you want 10 Gb in the future, and if the distance from the 1st floor to the basement is more than 55 meters, you'll want to upgrade from Cat 6 to Cat 6A.
And according to
this, Cat 7 is not a recognized TIA/EIA standard. The same article goes on to say, "Category 8 [is] . . . only for distances from 30 m to 36 m . . . . Category 8 is designed only for data centers where distances between switches and servers are short. It is not intended for general office cabling."
And according to
this, "10GBASE-T . . . provide[s] 10 Gbit/s connections over unshielded or shielded twisted pair cables, over distances up to 100 metres (330 ft).[44] Category 6a is required to reach the full distance of 100 metres (330 ft) and category 6 may reach a distance of 55 metres (180 ft) . . . ."
So once again, it seems like Cat 6A is your best bet if the distance is more than 55 meters.
But I'd measure the distance.