Dear Shells 2756,
I am going to tell you what I think, you might not like or want to hear it.
Call in the professionals.
You have not thought this new appliance installation through to its logical conclusion.
Let me explain further if you please.
Unless you bought some fancy dandy S/S sink the strainer basket are usually standard in size but as I am not there to eyeball this you are going to have to rely on the manufactors spec's or get away from the PC and go to a supply house like a Lowes, Home Depot to shop and compare. Whatever the case may be you want the strainer baskets to match the sink and the faucet.
The same applies for the apperance of the faucet, this is a matter of personal taste and how you feel about it and not how anybody else feels about it.
No, you do not need a garbage disposal to have a dishwasher installed, at least no local where I have ever worked or ever heard of, almost all the new dishwasher's have a grinder which breaks down the food particles before they are discharged.
You are installing a new fixture (dishwasher), this is not a replacement of an existing dishwasher, IE: this fixture needs to be roughed in, not only do you need a drain you also need a hot water supply and a GFI circuit for power and a permit needs to be pulled.
So needless to say the variables you are asking answers for are almost endless.
Septic or City Sewer ? sometimes a garbage disposal is not the best thing for a septic system, depends on age and type. Local Plumber can inform you as to options.
No matter which Plumbing code is in your area, you need to discharge the waste through an air gap. Which means if you bought a four hole sink because you want a sprayer, you are a hole short. 5 hole sink versus a 4 hole. You need another hole for the Air-Gap device.
What size is your hot water supply line to existing sink and type of pipe?
Where is closest electrical supply this would be a wet area, code calls for a GFI ? Electrical Contractor.
What type of waste pipe?
Is you new sink a single, double or triple bowl?
Please do not let the trim carpenter do this work, as I can see the rubber hose, clamps and 6 miles of extension cord now. LOL
This is your house and castle take care of it accordingly and it will give you years of enjoyment and pride