Hi, my boys are 3 and 4. I'd say do it this way:
1. Clear up
2. Sort boundaries (paint, clip hedges, whatever).
3. Hard landscaping. I'd go for a simple, preferably completely level, patio. Like you say, minimises mud dragging in. Mine use ours for scootering, and I have a builder's tray I put out now and again with play sand in for them.
4. Lawn. Prepare and turf the remainder.
5. Any other permanent features - trellis dividers, walls, whatever. I'd keep level changes to a minimum for safety reasons - its no good having a garden that mens mum's constantly running around behind the kids in case they trip - she should be sitting out there with a brew, supervising from her comfy chair!
6. Only after all that can you really start thinking about planting. You need time to assess how sunny or shady or windy or whatever certain areas are before you can choose appropriate plants. There's no rush - why not wait and see where your wife tends to sit - then site some beds where it'll give her either privacy, a good spot to watch the kids, and maybe a nice view. Maybe site another based on the view from the back windows. Maybe one to hide something you don't want to look at. Think about having a focal point for each of these 'key' spots. Maybe a small tree, or a large architectural shrub, or some other kind of feature. When you've got these bits planned to do their jobs, then think about linking them together. Do they work best as 'islands' .or should you connect them? Then think about planting. Start with the biggest plants and then fill the spaces between. Plant things either of decent size, or in decent clumps - nothing makes a small space seem smaller than a 'dolly mixture' border. Don't buy herbaceous plants in ones - for a garden your size, plant in 'triangles' made from 3 plants at a time. Also try to repeat a few of these triangles in different areas - it keeps it looking unified. Hardy geraniums are good for this - they'll grow almost anywhere so are likely to thrive regardless of aspect.
Anyway, that's how I'd go about it. If you didn't plant a thing until spring, you'll still have a useable, much improved space in the meantime, and you'll have had chance to research the planting. If you're really keen to get the planating fabulous, invest in the rhs planting combinations book. You start with one plant you wanna use, look it up, and it gives suggestions for things that look nice/grow well with it. Then look that one up... and so on. Definitely helps the novice a lot, and cheaper than buying the wrong things and ending up replacing.
Good luck, Bx