Turf? I hate to break it to you, but no grass is going to grow in that mudpile. Or any plant for that matter (unless it grows in a swamp).
Essentially all the water is running towards the house and that should be avoided at all times where possible. So I recommend adressing that first along with keeping in mind any hard landscaping you'd like (patio/deck, paths etc). This is where the bulk of your monetary investment should be and I recommend professional help aswell in my opinion. It'll set you off to do the rest yourself at your own pace and even on a budget can be satisfying.
Thinking ahead here: should the above mentioned recommendations of mine have been completed, I further recommend the following:
double digging, rototilling and raking level to get rid of any compaction in the soil (which is almost always the case in these situations, especially after heavy duty equipment etc has been on site) and to mix any possible occurring layers into a more homogenous soil type to accomodate water infiltration, but just ONCE! and mulch thickly afterwards (wood shreddings/chips are ideal and relatively cheap in bulk). All this will kind of reset the soil biome and with minimal maintenance/reapplication will develop further into a diverse and healthy soil ecosystem in which plants can thrive.
