I just saw your post…I would say a lot of that depends on your budget. If money is tight, I’d say put the majority of it into your lighting (which will generate a good amount of heat, themselves!) and ventilation/circulation. You might not need a propagation tray/warmer. You can germinate your seeds on top of the cable box or something similar, like on top of your fridge like you mentioned. Same goes for a heater. You might not need it if your lighting brings the temperature up enough. If it gets too cold at night for them to be in the dark, you can always run the lights at night, and have them in the dark during the day. Power is sometimes cheaper in the early morning hours, too. You can light your sprouts and seedlings under the same lighting you plan to run the mature plants under, start to finish-like. But some run smaller lighting that uses less power for germination, too. Just depends on your space and what works best for you.
As for soil and fertilizers, depends on if you want to grow organically or using synthetic nutrients. There are pros and cons to both. Organic soil/nutrients rely on a herd of microbes in your soil to break down the nutrients into a form that plants can absorb, whereas synthetic are immediately available to the plants. If you’re buying a fairly hot organic soil like Fox Farms Ocean Forest, it has enough in it to get you through the vegetative stage of growth, at least most of the way, possibly part way into flowering. Something with less in it out of the bag will require feeding sooner, obviously, but it also can give you a little more control over what you’re feeding. It mostly comes down to how hands-on you want to be, and how often. If you have the time to be in your garden more frequently, perhaps throughout the day, maybe coco coir is a better medium for you. It requires feeding right from the start, so there’s more required, more often, but the growth is also faster because of it, similar to hydroponics.
Regardless of the details of your grow, you’ll want to have a good way to measure pH of what you’re putting in, and what’s coming out, to monitor your plants’ consumption, and to help diagnose the problems you hopefully will have none of. Most use a digital pH meter or pen. You want to make sure it has a way to be calibrated, and solutions to do so. You might also want a total dissolved solids meter to measure what’s in the soil, as well as the strength of what you’re adding.
Haha, and what @LoCoRock said too.