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Are they stationary or mobile? Are they natural or artificial?

I was envisioning something constructed by the humans, sort of like B5. My desire is to keep things as hard and as low-energy as I can, even though it's obviously advanced theoretical physics, and in an ultra-hard universe like Orion's Arm it might be something that would take humans millennia to develop. As for traveling to new star systems, it would be either a) large dedicated hyperdrive ships that can travel there and set up the portals, or b) just using sublight ships to set them up, which would set a very strong limitation on where humans could go (i.e. a slowly expanding bubble of accessibility). And then the added possibility of hooking up with networks constructed by other alien races. I've been working on a reptilian race that would serve as benefactors sort of like the Vulcans, and an insectoid race that would be more hostile. (I also have a design for a big, mysterious, super advanced alien ship that I might throw in at some point - basically a Y-shape from the front, extending back hundreds of meters, with a sort of dark purple hull.)

I like the Stargate model as Reliant suggested, but my concern is, do you think the gates should require a constant supply of energy in order to remain open, or would they be more permanent? (Have they provided much explanation of that stuff in Stargate?) I'm trying to envision some big assembly in space with fusion or antimatter reactors attached.

Then there's the issue of where to put them. Earth orbit, or solar orbit at a stable distance from Earth? I'd prefer Earth orbit, but then there's the question of accessibility and vulnerability if you place it right next to your home planet. I suppose if it's a free, open connexion (like DS9's wormhole), that would be more dangerous, but if you can control how ships enter and exit, then it would be safer.

I'd really like to read up on a lot more sci-fi universes to get some ideas.

My take would be to have a natural phenomenon that requires a very large amount of energy to open. Originally a high energy deflector pulse (or something similar) would have to be fired to open it, which sapped energy from shields, weapons, communications and sensors. Obviously a negative quality. so a series of large stations were constructed around the natural phenomenon that fires the pulse for you. The "Gate Stations" would also be minimally armed, sorta like Trade Lanes in Freelancer, only they fire you at FTL speeds more like Trade Gates in the same game franchise.

I'm concerned about what to do with waste heat on my ships. What do you think of having large radiator panels (presumably of some very strong and efficient material) built into the hull around the ship's fusion reactors?

Your best bet would be to use the main engines as radiators - maintaining gravity, heating, etc, would be an insignificant fraction of total output compared with engines or weapons, so use them to get rid of waste heat. If you want station-keeping relative to another object, use fore and aft engines simultaneously.

You could go with the droplet system they use in Mass Effect, it would at least minimize the need for large, bulky and vulnerable radiators. Remember, the more stuff you put on them to armour them, the less efficient they'll be.

Also, turn off stuff you don't need in combat.