Hi, Kimberly here from landscape-solutions-for-you. Thank you for asking the question on your sloped yard.
The good news is your water flow going away from you home is correct. The first step is to make sure you properly prepare your ground as best you can. On a slope can be a little challenging to get the ground ready for plants and seeds. I do recommend top soil. Mulch will deteriorate after six months or so. You can put mulch around your plants once they are in the ground. A good quality top soil is a combination of sand, dirt and saw dust. These three mixed together can provide you with a good foundation for you soil (if you have that in your area)
I would also recommend that you plant your shrubs first. One of the problems if you plant your grass first, is the the possibility of stepping on the newly planted area. This will defer your seeds from developing. Once your plants are in the ground, create a good watering schedule to get them established. Go ahead and spread your seed. A good layer of straw or hay will help keep the moisture in the ground to get the roots established with your grass. Get on a good watering schedule with your new grass also.
I am not sure of your geographic location, but a good tip is to know your options in planting a warm or cool weather grass.
I hope this helps some and thank you again for taking the time to ask the question here at landscape-solutions-for-you. Feel free to let us know how you made out with your prep work, your planting and your lawn. Also, feel free to ask a question or two anytime. Have a wonderful day!
Kimberly