I will be doing my kitchen in the next year or so and for me I will make sure my sub floor is 100 percent up to grade to handle ceramic tile first. I won't remove old linoleum floor and instead go over top of this with plywood. Apparently you don't know for sure if asbestos was used in the lino so best to not remove it. Just so you don't get a Holmes on Holmes disaster you will want to make sure the plumbing, electrical and rough floor is done right and then move forward with the kitchen. So I wouldn't use a contractor and instead call in the pros by trade so I don't get a disaster. This may or may not cost more but you should get what you paid for.