Cucumber, carrot, avocado
Jalapeno, cream cheese
Fried tofu sticks, carrot, cucumber, lettuce (or bean sprouts)
Soy ham, pineapple, French's fried onions, teriyaki sauce, spicy mayo (our favorite from Sipz in San Diego)
Sweet potato tempura, teriyaki sauce (one of my favorites)
Basically just throw whatever you think would taste good together and give it a whirl. Other veggies include: bell peppers, raw zucchini, sauteed/marinated mushrooms, raw butternut squash, green onions/chives, daikon radish, asparagus, alfalfa sprouts, sun dried tomatoes, lettuce, steamed green beans. Also try fried egg strips, fake meat strips, goat cheese, or cream cheese. Top with panko, sesame seeds, teriyaki sauce, avocado, or spicy mayo. Making spicy mayo is as easy as combining mayo and siracha. Here's a YouTube playlist I put together to see how sushi is put together. It's pretty easy! It's easier to make sushi with the rice on the inside but I don't think it looks as pretty. I don't have a bamboo mat so I put these together with a clean kitchen towel and some cling wrap, no fancy equipment necessary!
You'll notice I haven't mentioned how to make rice. That's because it's kind of a lengthy and difficult process to make it correctly and I'm just too lazy for that. Realistically, you only need to worry about making sure you're using Japanese short grain rice so it's sticky. I just cook it how I normally cook rice and add some rice vinegar to it and break it up with a paddle. It's not the correct way but it works for me. It's actually really fun to make sushi at home so I hope you give it a shot!