I strongly recommend fixed price bids over cost plus or time and materials. Cost plus and time and materials put the risk of overages on the customer. They can cause the customer to micromanage you and pick apart your invoices. I have seen disputes over line items eat up enormous amounts of time and goodwill. Customers see your markup, so you can’t make it very high. If you are going to use them, cost plus and Time and Materials are best left for small, simple contracts.
Fixed price bidding requires careful budgeting, and you need reasonably complete plans. Use your knowledge to help potential customers make plans that fit within their budget and present them with alternatives. Get price-range decisions on the major items (cabinets, windows) before you bid and write the quality details clearly in the bid. Use allowances for smaller decisions like tile, plumbing fixtures, hardware. Give your client a list of decisions they need to make and a schedule for making them.
Even though your customer doesn't see your budget, track your job progress against the budget and learn as you go so you can make the budget better next time. That's the way you increase your profit.