I appreciate vastly different things about different friends, even though I consider them all good buddies.
For the person I consider my “best friend,” we have similar interests and views of the world. She’s lived across the country for the past four years, but we still visit every year and chat about every month. I’ve known her for a decade and a lot of our friendship is based on the fact that we experienced a lot of our formative years in college together. She was one of the first people I met at college, and we clicked instantly (I knew her roomate and saw her unpacking a comic series I liked). This is going to sound strange, but she is not a particularly kind person - but she is very artistic, intelligent, and articulate, and she’s taught me a lot about the world. We have similar family backgrounds, so we can commiserate over our ridiculous family situations together and not feel silly. We talk about art, literature, and pop culture a lot, but we also just “get” each other in a way no one else does. We used to spend hours at coffee shops drawing or writing stories together.
I have another good friend that we honestly have very little in common interest-wise, but she is just a sweet, caring person that is super social and full of laughter. I talk to her more than anyone else on the phone, by email, faceboook, etc. just because she is great about keeping in contact. I met her in college, and even though she also moved away a long time ago, we talk so often we’ve just bonded over everyday things and sharing our lives over the years. She makes a great effort to keep in touch, which is not always the case with people. I’ve had much deeper friends drift away as they never make an effort to stay in touch.
My current “same city” best friend is a guy that I used to work with, and now I work for his boyfriend. We started hanging out as coworkers and it developed into a real friendship. I consider both of them family now. We do have similar interests, but he is just a very kind person that is always there for me. We help each other out a lot and spend a lot of time doing activities together that we can’t find anyone else to go with - we go to the movies, road trips, hiking, kayaking, etc. We share a lot of the same interests, but not a whole lot. He is just a lot of fun to hang out with and he’s helped me through some harder times and I hope I’ve been there for him too when he needed it.
As to your last question, for me it is mainly an issue of continuing to make plans and being around the person. The longer you hang out with someone, the more comfortable you get with them and the more you discover, and the deeper the friendship can become. But it just depends on the person - I’ve got a brunch group that I attend every week (and have for the past two years). I consider them all friends, but none of them have ever become close. We just eat our brunch, chat and discuss current events, and then move on until we see each other the next week.