well first you can only start to pvp at LT 6 after that you can pvp all you wont. pvp is by level like only LT can fight LT and only VA can fight VA to make it fair. at all level you get stuff at the end of the match like cash, skill points, BO skill points, and badges that you can spend for gear at k7 but each tier has its own badge so if you are LC you can no longer get LT badges but can still spend them. ground pvp is not something i would recomend its not fun most of the times and most people really dont like it.
Is it primarily space or is ground pvp also an option/viable as you level?
Ground is theoretically viable, the problem is that the majority of players does not care for ground combat. I think ground PvP is probably more fun then ground PvE, but... Ultimately few people venture to try out.
Since you need people queued up for PvP to get a regular PvP match, ground PvP is a very slow and frustrating way to level up.
How fast do arena matches pop for space at the lt, lt com, and com levels?
If you're a klink it'll takes ages as there are very few klink players at that level.
As a Fwd it'll also likely take ages, because for some demented reason some Feds only que for FvK even though there's ever only one klink in the que. I've seen 9 feds and 1 klink in que for one match and 4 feds in a que for an FvF.