Assuming this is a premeditated murder and not a killing that just happened to happen, here are my thoughts.
One layer of cash-bought clothing from a second-hand store at least a month or two before the murder. An alternative option is stolen clothing from anywhere, but the key is that it has been worn relatively recently and is hard to trace. This first layer's main purpose will be to a) catch any DNA, shedding or stray hairs and b) be a 'getaway' outfit during the time period between the murder, my abandonment of my outer layer and my change of clothes.
This should include, but is not limited to, a transparent hair net (or shower cap, depending on type of murder); any kind of long pants excluding jeans; an indistinct long-sleeved shirt; gloves and long socks. Shoes will be flat and have no ridges or anywhere for dirt or other substances to lodge in and leave traces on floor. I will also include one random item of clothing that can serve as an identifier for pedestrians or whatever if I am noticed - something to draw attention to me without drawing attention to me. If they can focus on that and retain as little of my physical appearance as possible, then job well done.
My second layer of clothing will cover almost as much of my body as possible, mainly my head and any exposed areas where my first layer does not cover. Ideally this would be something baggy, something which doesn't look like it's covering up a whole set of clothes underneath. Easy to move around in. Something which provides a plausible excuse to cover my face/head and wear a full body outfit, like a plumber, an electrician or pest control. It's not that hard to replicate a corporate outfit instead of obtaining one - people rarely pay attention to what the labourer is wearing. Just obtain relevant, generic clothing and then customise it just enough so that it doesn't look generic but it's not a stand out outfit.
After the murder, outer layer of clothing is disposed of by driver and I burn or otherwise abandon or destroy the inner layer. If my house has a fireplace, get rid of the socks, hairnet and possibly gloves in there. This is assuming we're in winter. Everything else is shredded and either abandoned the day after or slowly but surely burned in the fire. Once I am done burning the clothes, continue to burn the fire.
Transport to and from the murder would not be my own vehicle or a vehicle I have any previous connection with - that would stay firmly put either in my house or somewhere else where it can be accounted for. Too many variables to consider with that. Ideally, a stolen, indistinct vehicle that is driven by somebody else or provided by that person. Obviously fake licenses all round. Unlike the clothing, this vehicle shouldn't be related to the company you're pretending to be. Make it look like a personal call for a low social class labourer, not an identifiable vehicle.
Person drops me off, once I am out of the car I make a comment to the partner that goes something like 'Hey, go get some (work related item), we might be a bit short. I'll get started on (work related activity).' That gives a plausible reason for the driver to not just be hanging around and looking suspicious for anyone that's hanging around. Go in, do whatever needs to happen for the driver to plausibly kill time. Driver comes back, I go get item from driver. Kill person and then leave. Vehicle is then driven to a) a crime-ridden area where car is likely to be 'taken out of my hands' once abandoned or b) far out area where it can be abandoned. Doors and windows left open so nature can work as quickly as possible and mess up anything we didn't clean up. Second vehicle in either scenario is in place and we move to that one, this vehicle adhering to the same criteria as the first one. Driver drops me off either at place that I have a plausible reason to be at or I am dropped off at area close to my residence. Driver then goes off and disposes the vehicle as he wishes or keeps it and cleans any trace I was there, along with taking my second layer of clothing with it and destroying it. I take care of one layer of clothing, he takes care of the rest. Dispersing all items used in the murder is key here so that the evidence is split up between us.
The murder weapon itself would most likely be a bendable wire of some kind, as strangulation is the modus operandi here. It silences the victim, is silent itself and is basically the perfect weapon as it causes death from the inside of the body rather than being messy. Generic, easily abandoned and only a minuscule amount of variables to work out. Guns have too many variables and are far too hard to work with. You're basically shooting yourself in the foot if you use a gun for a premeditated, up close and personal murder. Guns are only efficient for long-range murders if you plan to actually get away with the killing. Poison automatically stereotypes me as a female so I will avoid that. Plus, the wire works with the theme of leaving as little DNA as possible. Once I have murdered the victim, I leave the body as is except cleaning the area around the strangulation. If I have time, vacuum area. If not/it's too risky, leave area and begin getaway. It's too risky to move the body so I will have to leave it there, as moving it in a car is a big no-no. Impossible to fully clean the car of traces of the body plus there may be a scent to work with if police get involved quicker than thought.
After the murder, hot shower and full body cleanse/scrub. Wash hair, possibly get haircut. Change into new clothes. Change movie on laptop. I'll have had a laptop watching Netflix during the time I was gone, in order to make it look like via internet records that I was at my house. This is on top of all the other alibi planning I'll have done before the murder, but can't really go into here because it's too varied to detail for a specific murder. Just assume that I have thought out what I hope to be a clean alibi. Not airtight as it's suspicious, but clean and secure enough to leave me out of any true suspicion. Cease all contact with driver for at least a week after the murder, only meeting in person if we need to later on. Calling them, emailing them or otherwise connecting with them in any non-physical way is too easy to trace.
By the way, yes, I am the Zodiac killer.