125 I would not worry about what others say with regards to financing. I have two buyers right now in escrow, one with 5% down and another with 10% down. Yes financing is getting harder nowadays but no do not believe it is unattainable because somebody on a blog told you so.
I also have dog(s) and yes finding a suitable rental that is pet friendly was much more difficult then people make it out to be. Just be patient and keep looking around. Check Craigslist and the usual internet sites. Go to google and type in san diego rentals or strings similar to that and see what comes up. If you want to post your budget and areas you want to look at then put them in this string and I will see if there is anything on the MLS for you. The MLS is pretty weak when it comes to rentals but it does not mean it should be 100% ignored.
Now be aware of the timing we are (or at least) I am talking about. You should probably be ready to hunker down for a few years if you are looking to eliminate much of the downside risk of buying. Alternately you should be saving as much as possible. At some point we WILL see interest rates go up. Not if… when and by how much.
In terms of sellers paying closing costs that is pretty easy to get to happen nowadays. Anyways like I said, my rationale for not buying today has nothing to do with whether you can or cannot get the financing because you can. It is more along the lines of trying to recognize that you can save some serious bucks right now by holding off OR if you are gonna buy they lowball the sellers like crazy, then prepare for rejections, repeat the process, and you may get a hit if you don’t give up.