Seems simple enough, but I am going to start this with a background story. When I was in High school I had a teacher (shoutout to Mr. Long, he is a good guy) that also hunted deer. One day he made deer sausage and brought it to school (yeah I'm old and yes I can get on a soapbox and say today's generation is missing out on some very key old school knowledge). It was amazing. Years later I ran into him again and asked how he made it and it seemed easy. After that, I had a conversation with my grandmother on how to use a smokehouse, as when she was young they used a smokehouse to preserve food on the farm. I bought a few books on the subject and built my own smokehouse and that was a key aspect on how I started my quest for the art of the fire and where we are today.
The first batch I made out of the smokehouse was amazing and I couldn't believe this knowledge drifted away. The smokehouse is still here and we do occasionally fire it up in the late fall. But you can make amazing smoked sausage on a 1000 series. However, I will say, a proper cedar built smoke house is a very different environment than even a 1000 series and will give you different results than even a 1000 series. But if you're going to go down the smokehouse route, there's a reason why you want to build them away from anything else that could burn. Like your house. They're very prone to catching fire. But they're fun.
For the sausage, I'm just going to tell you to follow the instructions on the seasoning packet on whatever flavor of sausage you would like. With venison you're going to need to add a little fat or the sausage will completely dry out. I've tried all of the types of animal fat; bacon, uncured pork belly, duck, butter, tallow but the best I feel is still pork shoulder because of the flavor it adds.
Now for the grill part. Here we're going to use the firebox. My recommendation is to use a base fire of lump charcoal and then add whatever wood for flavor. If you're going for more sweet then 100% use a fruit wood. Cherry or apple would be very good. If you're headed for more spice, I'd stick to the hardwoods. Although apple is a very good wood with any sausage. Cook the sausage at 225° air temperature until it reaches 150°. Once you hit that temperature, transfer the sausage to the hot spot by the firebox to put a little sear and crisp up the casing. Make sure the sausage hits 160° before you pull off.
For the garnish, use olive oil and sauté up some red bell pepper, cherry tomatoes and some onion. Your hard work will be well appreciated.