Ok, you can put up something flimsy. Hmmmm. I am guessing that, like all of us money, and perhaps permanent fencing could be the issues as you are renting.
Here is what I did years ago, and I am sure it will be a little more expensive now, but definitely cheaper than something flimsy.
Go to Lowes or home Depo, and maybe tractor supply -- I know they have the fence pole tool. By some "T" posts and some rolls of horse fencing. About 8 years ago These were approximately $25 for a 25 or 50' 5' high role of fencing. The post hole thingy is a tool you put on top of the t or u-shaped post and lift it up and slam it down until the post is deep enough into the earth. I would figure a post for every 5-8' of fencing. They cost around $4. But that was a few years ago.
In my zip code at tractor supply, 5' studded T posts are $4.19.
5' x 100' of the horse fencing at tractor supply is $180.00.
Use your house for one side, and You can put up a 50'x 25' area. Figure 20 T posts at 4.20 each that's approximately another $100. And you might find this stuff cheaper -- this is NE Ohio -- not too terrible far from you if it is cheaper here.
You will need a gate. My dad and I built a gate with wood and some horse fencing. I do not suggest this. I suggest ordering a gate panel for the Doc Bob Kennel system from tractor supply. It will cost $100 and they work great. It is 5' wide and 6' tall, and most of that is gate panel, so you can still get a lawn mower or wheel barrel through it.
Ok, now is the trick. GSDs have been known to dig or climb. If you go out there with him every single second he is out there, then you needn't worry about it. Your obedience will be fine to keep him from molesting the fence. But if you do want to let him out here and there on his own, then this worked great for me:
I bought a small solar powered electric fence and a roll of aluminum wire.
Hope the link works, but the solar charger is still $99, the aluminum wire is $26, and the t-post insulators are on that page, I think a couple of bags of them would be plenty -- 8.99 each.
Got to run now, but total cost to have a nice fenced in area -- and you can make it larger by adding more horse fencing and t-posts -- the electric fence will go for 2 miles -- will be, roughly, $525.
The nice thing about the electric wire is that the dog can see it and will adjust himself before reaching it. Mine would rush to the fence, stop, look for the wire and stay away from the wire. They respected it. I no longer have my wire up, as they learned to leave fences alone. Install the fence at least 12 inches off the ground so you can weed-wack the fence.
Hope that helps. Good luck. Other places might be cheaper.
ETA: it isn't permanent and can be uninstalled and will leave no permanent marks, so your land lord should not have an issue with it.