Homeowning and renting DIY pest control are two separate beasts, I've learned. It feels practically impossible to DIY it when you are renting and are connected to neighbors. If they don't care about prevention, then the pests will wander into your place too.
I owned a house for ~5 years (don't own now - I hope to again soon) and the only ongoing "pest" problem I had was crickets would get into my basement at night sometimes. They would ultimately die if they stayed too long because there was nothing for them to eat. I didn't really see the need to try to kick them out because they weren't breeding in the house, negatively impacting the structure itself (like termites might), or trying to eat any food. They also weren't exactly being attracted to anything in particular.
I did occasionally get field mice in the house. I had then (and still do) a pet cockatiel so felt uncomfortable at the idea of spraying or laying out any poisons. What I did instead was trap the mouse in a room and vacuum it up with the ShopVac and dump its dazed self out way, way down the street. I only had this happen maybe twice, and it was a single mouse each time, so I didn't have to deal with trying to get out a whole family - thank goodness.
I once got ants. They were attracted by something in the kitchen. I can't recall what now. You can mix water and dish soap to clean up their scent trail and then use vinegar to deter them. Again - that's a non-poison, pet-friendly solution that works well. Once I did that and made sure to keep the kitchen clean of anything that might attract them, ants never came in again.
I never had a roach problem in the house I owned. But I've always tried to keep the kitchen clean, food put away, and not keep trash that has food scraps in it in the house for too long.
I never paid for pest services. I absolutely would have if I had termites or something though.