Good morning Mike and welcome, If you could post some pictures of your smoker it would be helpful. A typical off-set has a cook chamber (CC) and a fire box (FB) I am guessing you have a strait flow (SF) (fire box on one end and smoke stack on the other. A reverse flow (RF) has the fire box and smoke stack on the same end. First lets get your smoker seasoned up before you smoke anything. Get a can of pam (any spray type oil) or a spray bottle with cooking oil. Next you need to build a fire in the fire box, charcoal, lump charcoal either is fine. if there is a damper between the FB and CC make sure it is wide open, if your stack has a damper open it all the too. Now your are going to start getting the smoker up to temp and a little more. Let it go like that for a little while, it will take care or any surface oil that they sometimes use at the factory. Then you want to spray the entire inside and racks with the oil. Let it bake on for a while and I would spray it again, just let it go till the coals got out. and your seasoned up.
Now what to smoke first ? Since you are new to smoking, do some chicken I like leg quarters, pretty simple, cheap and real forgiving. Build your fire in the FB , while your smoker is coming up to temp, we'll get the chicken ready. I like to brine my chicken but we'll save that for another time. Clean you quarters up, rub them down with olive oil (or any good oil) coat them with your favorite rub, and they are ready for the smoker. There are all different suggestions on what temp to cook chicken, I smoke at 225º to 250º low and slow. So assuming your smoker is at 225 -250 throw a few chunks of whatever flavor wood you prefer, Your chicken will absorb the smoke flavor, Leg quarters should take about 3 hours or a little more you want the internal temp to be at least 165º If your chicken looks like it is drying out you can spritz if (I use apple juice) when its ready should be somewhere between a deep golden brown to a light mahogany, tender and juicy. When you take it up let it rest a bit, the juices will re-distribute and won't run out when you cut into it. Hope this is helpful and gets you started in the right direction
Gary S