Hi there. I am a CFI in WA and have been flying both civlian and military in the state for the last 13 years. I have taught at several different schools, and I should be able to give you a good idea.
#1. When you say Seattle, do actually mean Seattle proper? A lot of folks say Seattle when they mean Everett or Tacoma because no one knows where that is.
I can offer a few suggestions.
First, understand that you are going to need more cash. A PPL alone will probably take a good chunk out of what already have saved. That being said, with the weather getting better and you having the funding you should be able to start now and be flying by yourself by the summer if you are dedicated and don't screw around.
The question always comes up, school or club? I think you get a better bang for your buck with an established club. You could look at Evergreen Flying Club out of Renton, or Valley Fliers out of Auburn. I have worked with both of them and they are good, well established groups with a robust CFI base of folks who know the area well.
Schools. Anything established at BFI is going to be expensive. So, I would avoid. You can look at Alternate Air if you want, but be sure the equipment is solid. I haven't worked with them in years.
Renton has three schools: Pro-Flight, Rainier, and BEFA. Personally, I would go with Rainier to start. They have newer, albeit slightly more expensive equipment but they seem a little more 21st-Century geared.
15k should be enough to get you through a 141 ASEL IFR Program. After that, you are going to pretty much be on your own to get the required time to move to commercial.
Like I said before, don't screw around. The spring / summer flying season is here. Fly as much as you can during the week and don't scrimp on ground lessons.
Don't finance. Do you hear me? DO NOT FINANCE. Do not beat yourself into debt for an industry that isn't paying a livable wage for what you had to do to get into it. Work like hell, save up, and pay cash. That way, when you have all the ratings and no debt, it won't matter what you are making.
No one cares what your time is in. Fly the hell out of a cheap 150 or 152 to build total time.