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I agree with the first two comments, very good advice.
Here's some other things you might to consider:
You want to make sure that are able to make an apples to apples comparison with each of the estimates you receive. If one estimate is more detailed for example, ask the other contractor if their estimate includes these details that their competitor is offering & will they be willing to include it in writing?
Ask for 10 references instead of 3. The reason I say 10 is because this will give you a better sample size of the contractor's experience and track record. Anybody who has been in the business (especially siding which has many annual clients) should have no problem giving you 10 satisfied, recent clients. Granted you don't have to call all 10 but even the worst contractor can probably scrape together 1-2 "positive" references.
Go to their website. This day and age they should have a website. This should have pictures of their siding projects to view. They should also list their certifications and which products their install.
Go with your gut! If a deal seams too good to be true it probably is. After you do your due dilligence be honest with yourself and choose the contractor that you feel you can trust and will provide the best product. Don't just use price to make your decision.
About 6 years back we installed replacement shutters on a 1930's era home. The origonal wood shutters were painted black but had serious rot issues after years of enduring the wet conditions of the Pacific Northwest. We decided to construct the new shuters with Azek PVC. Our Azek Rep. recommended that we use Sherwin Williams VinylSafe Paint. It resists UV heat gain and the shutters we installed still look great. Good Luck!