Hi! I am not sure what you are considering inexpensive, but I live in a "small town" area of Orange, CA. I pay $1,800 a month for a two bedroom with enough yard for our dog. The utilities are very cheap - water is almost always $36 every two months, gas is always $12 a month, electricity was $44 this month, but we ran the AC almost constantly! Of course that'll vary on your usage but our prices are consistent to the dollar for some reason, lol. There is a dog park nearby, too, and good vets all over. For food, we drive about 20 minutes to WinCo, that has the cheapest groceries I have EVER seen. They have EVERYTHING, too.
I've had no issue with being trans, but I am not out to really anyone in the area. However, I rented a house with no trouble and my landlords refer to me by my preferred name and pronouns, yay! I pass more often than not, but when I don't, a polite correction never goes without an apology. It's a very LGBT friendly area. The Gay & Lesbian Center OC is nearly within walking distance, and the Gay & Lesbian Center LA is a half hour drive (in good traffic). It is where my boyfriend and I get hormones and it's VERY affordable - they're very open to people with bad insurance, no insurance, etc. The transgender law center is also nearby.
My area is actually right by Chapman College, so it's a lot of college age people around, if that bothers you. However, we only had noise problems one night, and it was a holiday weekend. The Orange Circle is right nearby, which has a ton of adorable antique shops and things. The population doesn't feel crowded to me - you see people walking around the shops and to school, but there is no bad traffic around the streets, no crowds, etc. Disneyland is nearby but not so close that you get those crowds!
Overall, I LOVE it here - and I'm like you, living with my SO with three children with paws, definitely like my privacy. Trans health care has been a breeze with the Center LA nearby - they will ship you hormones for FREE!! Like I said, I don't know exactly your price range, but if you can afford it, I think the area is perfect for your needs.