Bison, remember also, you can create chokepoints and cuts of entire arms of star systems. That means that it's impossible or very difficult for others to reach and colonize them. If you have closed borders, then no one else can reach them. But even with open borders, they have to spend a lot of influence to colonize a single system in that cut off area.
Unless there is a system I really need, I'll leave those cut off areas until after I've got my outer borders established.
When establishing my outer borders, I always look for a single system chock point. Meaning that anyone trying to invade has to come through that single system. I'll explore as far as I can past that point, and sometimes I'll have to make decisions if I should grab a particular valuable system and lose the single choke point gateway. If I cannot get a single system gateway, then I want the two systems connected with a hyperlane so they can support each other with a single fleet.
This is from my current game, if you look, there are 3 arms that are cutoff from others. I'll collect them when I time/resources to do so. Also, I'll only push survey work in they areas as I have the science ships to do so.
Let me know if you have questions of points you need clarified.