Remodel can mean adding electrical and and sinks and a toilet or it mean finishing the walls and ceiling and floor. Two very different situations in terms of complexity and permits needed.
If you are just covering the walls you can get a drywall contractor to give a quote or for a drop ceiling a ceiling contractor but when you get into adding electrical and plumbing you need a remodel contractor who uses his or her own people and may sub out portions (like the sheetrocking).
With any contractor I would want to talk to the home owners on the last two jobs they worked and find out about the quality of the work, how timely they were in getting the job done, and any problems with the materials used or the people on the job or cleaning up after themselves or in scheduling of the work. Often general contractor add on their 20% but do not actually supervise the workers on the job so you are not getting full value for your dollars.
You will be dollars and grief ahead by taking time to talk to several contractors and letting them know what you find to end up with and how they would suggest getting their and the cost and time involved. There are always multiple approaches and talking to multiple contractors is the best way to determine what they are and then at least you will be making a more educated choice as to what to do and who to hire.
I would not rush the project through but allow time to make alterations based on what is found on the job as it proceeds. Everyone hast their own opinion but for a remodel such as this I would hire a general contractor who will be responsible for everything and then spell out in the contract exactly what work will be done and what materials will be used.
The very real risk is that often you have to pay a general a large amount before they will start the work and if they turn out to be incompetent you will find it virtually impossible to get any money back. If the general contractor does not pay the sub contractors you will be on the hook legally to pay them.
There are lots of quality contractors that might have considered your job too small in the past but will now be happy to get any work to keep their people busy. So I would start with the top remodeling firms in your area. Often architects will recommend people that they have found to be honest and reliable and competent.