I’ve never done any serious mulching. Now I want to do the perimeter of the lawn to make mowing easier.
So, questions:
Should I kill the grass first or just put mulch on top?
How thick should I lay it down?
Does the type matter? I’m looking at something pretty basic, dull grayish brown. Is any type better at stopping weeds or longer lasting?
Should I consider the recycled rubber stuff?
What else should I have asked about?
If you just put the mulch on top, the grass will grow through the mulch. I’d kill it or else put down a barrier of many sheets of newspaper before putting down the mulch. (If you can find newspaper any more these days.)
ETA: Do you have any edging? Grass has rhizomes, and will spread into adjacent areas if it can. Even with edging, it can still get in, but not as bad.
You’re going to need to dig down a bit so can have a few inches of mulch, then you’re going to need some sort of barrier, either plastic or landscaping fabric to keep the weeds at bay for at least a few years.
If all you do is toss mulch on top of live grass, the grass (and wees) will grow through it in a matter of months or weeks. Also, if you don’t dig down, you won’t be able to put a very thick layer down (unless you’re going to mound it up really high) and it’ll decompose really fast. Even at 2 or 3 inches thick, you need to add more every 4 or 5 years.
Another thing, a good border (like one of those hard plastic ones) will make a huge difference at keep a line between the grass and the mulch, otherwise they’ll just meld together over the years.
BTW, are you planning to keep the mulch the same height as the grass or are you planning to mound it up a few inches?
I planned to mound it up, some. I figured this was the first layer and wasn’t going to go too thick. I wanted to see how it looked, and what I might do in the future. So I might add more next year. I was thinking about edging. Didn’t know if I should do it right away or wait. I might do something with stones or bricks, just depends on how it looks. I didn’t really want to dig down, my knees are bad and I’d have to find someone to do that. Most of the edge of the lawn is in shade, rocky, or covered with pine needles, and grass doesn’t grow there well anyway. That’s one reason to do this, it’s a constant battle between weeds and grass.
i don’t have mulch advice. well maybe a little.
you want something that you can run the mower over and still get a cut on the edge, as if it were a sidewalk. so raised might not be good or something the blade would hit. bricks can shift up or down as well as edging. stones can get propelled by the mower.
wood chips level with the ground would be best. it is extra work though you have sod that you can relocate, some top soil you can relocate.
Mulching over areas that aren’t growing much grass anyway is a good idea. I have put a bunch of pine cones under my spruce tree in front of my house, and it looks much tidier than just having a bare spot there.
I agree with edging of some kind between the mulched and non-mulched areas, though - as others have said, grass does send shoots out, and the mulch can also be hard on your lawn mower (judging from the sound it makes as I go over it, anyway). They do have hammer-in edging that you can use - just like it sounds, you just hammer it in with a rubber mallet and viola! it’s all edged up.
You want a fairly serious layer of mulch, too - three to four inches to retard weed growth. I like a mulch made of cedar or pine bark that is chopped pretty fine. I’m finding that you don’t need to replace it every year, but it doesn’t hurt to top it up each summer - the mulch does degrade, and it gets patchy. It also looks really nice when you put a fresh layer on top. 
Ok, black plastic is easy to lay down, and then a few inches of mulch on top. Even without edging that will be fine for most of the perimeter where everything is kind of rough. There is a long run of thick grass on one side where I have to consider digging down. This is where it affects the mowing the most, and I have to keep it from spreading into the neighbors yard. I have a free standing tree and some bushes to encircle, not sure what to there yet. But they aren’t a mowing problem, so they’ll probably get done last. Stones for edging are out, I don’t want to replace mowing with more weedwhacking. Maybe setting bricks into the ground for edging in the nice areas will work out. I figure I can get a couple of yards at a time in the pickup truck, and dump out piles where it will go, so it will mostly be a raking job onces everything is prepped.
I’m not sure what your mulch options are, but in the Pac NW, the most common types are Douglas fir and hemlock. Doug fir tends to be cheaper, but you get a lot of splinters if you are spreading by hand or weeding in it often. We prefer the hemlock.
You probably have totally different option in RI, but it’s worth asking about stuff like splinters in the types available to you.
You also need to think about rain wash out. If the mulch is just loose on the ground without much to hold it their, (i.e. brick pavers, some sort of edging, grading using gravity to hold it in, etc.) then when you have a heavy rain, a lot of it can be washed away.
Be careful of what mulch you get if you’re going to buy it buy the truckload - my neighbour put down mulch like that, and it had every weed known to man growing out of it two weeks later.
weeds will come through thin mulch. if the mulch is thick no life supporting soil or water is near the top.
If you’re going to use a barrier, landscape fabric allows air and water to be available to the roots. Plastic does not, and if there are not enough holes punched, the accumulating water can carry the much away.
Roots naturally grow at their preferred depth in the soil and putting too thick a layer can cause them to grow up into the mulch, where they are much more susceptible to drying out and being exposed by erosion or decomposition. I try to maintain two to three inches, no deeper, and not to the trunk as it can cause rot by holding moisture against it. It can also create shelter for pests to eat the bark undetected until it’s too late.
In a zone with cold winters, it’s a good idea to mulch after the ground freezes rather than right before. The goal is not to keep the soil warm, but to maintain a consistent temperature. Alternate freezing and thawing is a problem for several reasons.
If fresh wood chips are used, a cheap nitrogen fertilizer should be added to the root area of desirable plants to replace the nitrogen depleted by the decomposing process.