If it's that bad? Start over (although fall is a better time to do that). RoundUp isn't exactly perfect, but at least you only use it once. Then even it out, then finally try for a lawn.

Well, since you said you welcome any and all suggestions, I'll tell you what I think based on the limited information you provided and the limited knowledge I have.

It sounds (to me) like you're embarrassed by the present state of your yard and want to rapidly turn it into a source of pride rather than an eyesore. I think that can be done in a matter of weeks if you have a little money to invest in the process.

First, I'd get a soil analysis completed to find out if your existing soil is suitable for sustaining healthy turfgrass. You probably have a very acidic soil and possible compaction problems if your soil is mostly clay. The results of your soil analysis should include recommendations for amendments such as organic matter and/or an application of lime to neutralize the Ph.

Second, I'd hire a landscape contractor to level your yard (I really don't think this is a job you want to tackle yourself) and incorporate any soil amendments recommended by your soil analysis. This process should churn the existing, unwanted flora back into the soil to decompose naturally, obviating the need to apply Roundup and keeping Lake Washington safe for the salmon.

Third, find and install a sod with a blend or mixture of turfgrass varieties adapted to Seattle's climate and the hours of sunlight each side of your house typically receives. If you have moss in your yard now, that may be an indicator some light-loving turfgrass varieties won't thrive on that side of the house.

I recommend sod because you seem eager to get something down that will look nice as soon as possible.

Fourth, fertilize your new turf using organic means to further protect Lake Washington from harmful chemicals.

I have no idea whether turfgrass in Seattle needs supplemental water. Intuition tells me no, but I could be wrong. If your lawn is small, as you say, you can probably get away with just using a hose to apply supplemental water as needed. You'll want to keep new sod from drying out as it's establishing, but at this time of year with cool temperatures and Seattle's rain that's unlikely to become an issue.

I'm going to add clutter to the information you have already received. Definitely fall is the best time to reseed. If you can stand you yard for this season, you will be much happier overall (I think). Basically if you have never had grass before, you need to start with the basics. If you follow these steps, you may not want to do anything come fall.

2. Water deeply and infrequently. Deeply means at least an hour in every zone, all at once. Infrequently means monthly during the cool months and no more than weekly during the hottest part of summer. If you get an inch of rain, don't water. If your grass looks dry before the month/week is up, water longer next time. Deep watering grows deep, drought resistant roots. Infrequent watering allows the top layer of soil to dry completely which kills off many shallow rooted weeds and prevents most weeds from germinating.

3. Mulch mow at the highest setting on your mower. Most grasses are the most dense when mowed tall. Bermuda, centipede, and bent grasses are the most dense when mowed at the lowest setting on your mower. Dense grass shades out weeds and uses less water when tall. Dense grass feeds the deep roots you're developing in 1 above.

4. Fertilize regularly. I fertilize 4 times per year using organic fertilizer. Which fertilizer you use is much less important than numbers 1 and 2 above.
   

The longer you take good care of your weeds, the better the grass gets. As far as tools go, you might want to start with a Weed Hound ($20 almost anywhere). If you want to watch your chemicals, flip over to the Organic Gardening forum and find the FAQ for organic lawns. Organic lawn care is not expensive, does not smell bad, and will not smother your grass with tonnage of compost. You don't have to tolerate weeds or pests either. There are so many untrue myths about organic gardening.

Oh I forgot. If you want to level your yard (preferably next fall before seeding), definitely get a professional landscaper. Leveling for turf is not something you can do with a tiller. I know every lawn book says to use a tiller but they must be high. Using a tiller is the reason why your lawn is uneven. Tilled soil never settles evenly. That's fine for a veggie garden but not for a lawn. If the landscaper shows up with a bobcat or skidsteer, send him back to get a real tractor (big wheels on the back, little ones in front) with a box blade (also called a landscaper's blade) in the back. A pro can finish a normal (no sprinklers, trees, patios, decks) yard in a morning with the right equipment. The bobcat will take a week to get it right and then it won't be that good. The box blade will not dig deep to reincorporate the surface vegetation. It scrapes the surface about an inch deep and redistributes only the tops of the hills to the bottoms of the dips. This leaves your underlying soil structure intact. This is an important difference between tilling and scraping.

I usually disagree with soil testing, too. They always recommend the same thing (add organic matter and nitrogen and adjust the pH). Unless you know of a recent chemical spill, simply get going on an organic fertilizer program and see how it responds. All three issues from the soil test will be cured by the organic program. But even on an organic program, I would not spend ten cents on compost. Unless you have tried everything else and the grass does not respond, compost is too expensive. Just fertilize as described in the FAQ and your organic matter, nitrogen, and pH will improve like magic. Your soil microbes are the organic matter that matter. By fertilizing with organics, you will be feeding them and allowing them to multiply and help you take care of the yard. Read the FAQ for more info.