Running! My favorite of the three tri sports because of it’s simplicity. You can literally run out the door in your birthday suit and go for a run. In other words, you don’t need anything to run.
For any distance, a good pair of running shoes is a great idea. It’s also good not to keep them around too long or your feet, knees, or something else may start hurting. And clothing can be important. Watches can be fun, other tech such as a heart rate monitor. But, it’s certainly relatively simple to get your run training in.
Maybe you like running on a treadmill? Or maybe you dislike it, but when it’s really cold outside, you choose it as your best option. If trying to save, you could consider a gym membership only in the winter. Or purchasing a used treadmill if you have room at home. Many places also have free or low cost indoor tracks that may serve your needs. Or, depending on just how cold, investing in some cold weather running gear or even switching to cross country skiing part of the winter. Or, perhaps your tri goals are such that you don’t need to run all year, or at least not so much that you can’t wait till a break in the weather to get out.