Well, there is no one right answer. First you have to figure out what your over-arching strategy is. Are you going for a full espionage-economy? Are you simply trying to supplement your normal research economy with a little spying?
I'm going to assume the former, from your description. From this point of view, no, you don't have to get the Great Wall, it just gives you some extra GSpy points you wouldn't otherwise have. You can run Spy specialists in your cities and use those to get GSpies as an alternate method.
Switching from research slider to espionage slider should happen somewhat soon after you get Alphabet - which you should have bee-lined (beyond the immediately necessary worker techs). The trick is to decide who is going to have the techs that you want to research, and focus your EPs on them. Do not use any GSpies to infiltrate the enemy! Do not settle your GSpies! When you are going for a full Espionage economy, using GSpies to build Scotland Yards is the most powerful use you can make of them. Build SY in your top espionage cities, and you'll easily get more EPs from them than settling/infiltrating would ever give you.
Remember that there are a lot of buildings that have low or no priority because of the espionage focus. Libraries, Universities, Monasteries all have extremely low priority. All they really do for you is give you extra culture - nice, but not a ncessity. The research bonus does nothing for you. So save your hammers for building spies - don't bother building those buildings.
Once you've made your focus on espionage, the only necessity is to keep track of who's doing what. You'll see what everyone is researching, so it'll be easy to figure out who you need to steal from next. You'll see what everyone is building, so you can tell if someone is building a wonder you are thinking of trying for. And if they are, so what? You can easily afford to trash their building so that they never finish. You'll be able to see all their cities, so you can easily see how much research they are generating, what they are defending their cities with, what cities have their wonders, etc.
Spying is incredibly powerful. The only real downside is that because you never research anything yourself, you don't get any of the benefits from being "first" to a tech (religions, GP, free techs, etc). But that is more than offset, imo, by the fact that you'll be able to track what everyone is doing. Knowledge is power!
Bh