Okay, so this is how I make chili. I put olive oil in a big pot and put it on the stove at about 2 or 3 (med-low). I chop the onions fairly coarsely and toss them in, and then I do the same with the celery. Mince the garlic, toss it in. Stir a bit, and then get out your peppers.
I've read up a lot on the peppers. Our local veggie stand has a bunch of different kinds in the summer, and I've taken to growing them. I like to use one anaheim or poblano, and one hungarian hot wax pepper. (I don't like the taste of jalapenos, so I don't use them.) I go for what I consider to be a medium heat, although to my family it's too hot. I suggest reading about peppers and experimenting to see what you like.
So I cut the peppers in half length-wise, pull out or cut out all the membranes and seeds (these will make it hotter if left in), and then dice it up to a medium mince. I tend to get lazy, so the first one comes out well-minced and the second is usually chopped a bit bigger. Toss those into the pot, and stir everything up some more. Cook this up until the onions become transparent and soft, and then start tossing in your meat bits.
I started out using stew meat, but it was never chopped small enough for me (I choke on big bites) and it tends to be low quality meat. Plus I found that whatever steak was on sale was cheaper than the per-pound cost of stew meat, so I started buying steak and chopping it myself. I like pieces that are an inch cubed or smaller, and I try to pull off the fat and gristle. You can use beef, lamb, pork, or even turkey if you want. whatever you like or have available.
Cook the meat in with the onions etc. until it's turned grey, and parts have browned. When you're satisfied (it doesn't have to cook through all the way), open up the cans of tomato products (including the paste) and toss them all in. Note on the tomatoes: I like tomatoes, Mr D is allergic, so I tend to use tomato sauce so he doesn't make faces and pull out chunks of nasty icky tomato. I prefer it with chunks, myself, but it's good enough either way. As you prefer. Put some water into the tomato cans, a quarter to half full, and swirl around to get the tomato off, and then toss it all in. I generally add two cups or so of water, at this point.
Which type of beer you use depends entirely on what you like. Using porter or other dark beers like that gives an interesting flavor. Usually, I use whatever beer I'm drinking. Redhook, Alaskan, Henry's, whatever. I don't think I'd use a flavored beer (like the pumpkin ale or Hale's Apricot Ale). Cheap is just fine. Open it up, take a slug, and then dump half to three quarters of the bottle in the pot.
I do not measure my spices, so this part is approximate. I use a couple spoonfuls of chili powder, and then maybe a teaspoon each of the coriander, cumin, red pepper, cinnamon, and oregano. Toss in the bay leaf. Paprika is a dash or two, same with salt and black pepper. I put the bouillon cube in the empty tomato paste can with some of the beer or some water and let it sit for a while, then stir it up a lot to get the paste off the can, and toss it all in. Throw in the bay leaf, and stir it all up. Add some more water or beer if it's not thin enough; remember it needs to cook for a while and you'll be adding more stuff to it. You want it pretty soupy at this point.
I don't usually add the vinegar or lime juice until after it's cooked for a while. I have a vague memory of reading that the acid will toughen the meat if it's cooked too long together, so I don't put it in until near the end. At this point, just stir every fifteen to twenty minutes and let it all cook up for as long as you want. Minimum is half an hour, maximum is whatever as long as you keep adding water. I like to let it cook for at least an hour.
When you're liking the thickness and smell of your pot of red, get out the beans. I have cooked beans from dried for chili, but I'm not usually organized enough. I like to use two different kinds of beans in my chili. Pinto, red, pinquito, black, kidney, whatever. I've used navy beans too. Black eyed peas don't work for me, but it's up to you. I usually have either pintos or kidneys, and then one of the other ones. One can of medium to big beans (like kidneys), one can of medium to small beans (like black beans). I rinse them some, and then dump them in the pot. Stir it up, and maybe now add your vinegar or lime, and let the beans warm. This is also when I toss in a cup or so of frozen corn kernels, because to me it's not chili without the corn. Another one that is up to you. This is also where you make sure the texture is right, whether you like it soupy or really thick. It's pretty amazing how much the beans will thicken it even if you don't cook them until they dissolve.
Let it warm through until the corn is hot, and it's ready to serve. I serve my chili over white rice, with grated cheddar, sour cream, and chopped cilantro on top. Some people like olives (I don't), and I will occasionally chop some fresh onion to go on top. I also serve it over pasta, like elbows or shells, if I'm feeling like it. I almost never have chili just plain, I have to have some kind of starch with it. And cheese. The rest is really nice, but I'll still enjoy it without. Some people like crackers.
Feel free to ask questions. I have three chili cookbooks, which I'll sometimes pull them out to look for ideas. But this is how I cook chili when I want a pot and don't want to think about it. I'm pretty casual with the spices. Oh! And I acquired a bag of dried hot red peppers at the store a while back, which I've been using instead of fresh now that the season's over. I use three of them (they're about two inches across the wide part and maybe three or four inches long). Pull them into pieces, ragged and uneven is just fine. Remove the seeds, stem, and pith. Put them in a bowl, pour over boiling water to cover, and let them soak while you do all the chopping. When they've softened some, put the whole mess in the blender and make puree. Toss that in the pot when you're adding all the spices and tomatoes, and you're all set. I have no idea what kind of chilis these are, but they work pretty well. They come in big cellophane bags with labels all in Spanish. I think they might be New Mexico chilis, but I can't tell.