One common recommendation for soil pH is 6.0 to 6.5 for roses. I wouldn't be concerned at all with a soil pH around 5.8. Planting time is your one good chance to improve soil structure with organic matter and most compost tends to raise the soil pH and also tends to make pH less critical in terms of plant availability of soil nutrients. The Roses Unlimited recommendation calls for about 50% organic matter (peat and compost combined). I wouldn't go above this ratio with more organic matter, you'll just get a lot of soil settling as the organic matter decomposes. You should also check and see what the pH of your township compost is. If they can't supply this number, maybe they don't know what they're doing. Also, unless you use lots of peat moss, I wouldn't add the cup of lime recommended by Roses Unlimited - that's just to neutralize the very acidic peat moss in their recipe.

I wouldn't add hay either, unless it's composted.

50% organic matter is a lot, even for clay soil. It does lead to your soil settling as the OM is eaten up. So definitely don't use more than 50% and don't agonize over getting exactly 50%. I usually add about 1/4 organic matter, whether to clay or to gravel (which is what I'm gardening in now). I like compost, leaf mold, and composted chicken manure for my roses.

Here on the West Coast I do not recommend using peat moss because of the way it reacts to soggy winters and bone-dry summers. Plus, my soil here is more than acidic enough as it is already without adding peat moss. I hear it's ok on the East Coast, probably because of year-round rain, but I'd still be wary of its effects on your pH.

You can get a soil test kit at any nursery which will be good enough to give you an idea of what your pH is as well as nutrient levels. You could add bone meal to the planting hole if your soil is low in phosphate, but for the most part adding compost and manure adds all the nutrients you'll need.

5.8 sounds fairly high. I expect the previous owners limed the lawn to get it up that high. I wouldn't worry about it, but definitely keep an eye on pH. For that reason, I'd avoid peat moss, as well as it's undesirable water qualities. It's just not necessary.

When we lived in Easttown, the municipal compost was essentially leaf mold. There may have been other stuff in it, but not very much.

Do not worry at all that it's heavy clay. Roses like heavy clay. If you go out of your way to make it too light, you'll be doing a lot of extra watering. Given the almost annual water restrictions, this is something to avoid if possible.

Thanks!
Btw, how important is adding alfalfa when I plant?

Hardly anybody added alfalfa until the past few years, so it's certainly not essential. 1/2 cup mixed with the soil right around the roots might help the plant start faster, but there has been no scientific trial that I'm aware of. I use it.