Why is it important to sequence your plasmid after purifying it?

Here is my suggestion. ALWAYS you digest a vector you should do a gel-purification step. Some people will say that they don't do it because it's a waste of time and that is ok, however, if you do it you are practicing good molecular biology as defined by Sambrook&Maniatis, and these guys knew something about it. Therefore, I will encourage you to do this step as often as you can, this will ensure you have no traces of undigested vector that will interfere during your transformation step (e.g. false positive) and consequently save you time later. The best way to save time is to do it right. You also want to get rid of buffers and ions that may (or may not) interfere with your phosphatase steps and have a clear start too. The later is not so critical though, as most reagents are now quite compatible with each other as well as between companies, which is great. Then, after phosphatase treatment the cleaning step depends on two things: if you used CIP (NEB), this enzyme you MUST gel-purify (recommended) or use a kit to get rid of the CIP that tightly binds to the end of your DNA and cannot be heat inactivated. If you used TSAP (Promega) 0r any other thermosensitive phosphatase, then you can heat inactivate it. The next thing to take into account is to check the buffer compatibilities between your recently 'phosphatased' vector, your digested construct and your ligation buffer. Most of the T4 DNA ligase in the market are compatible with any of the buffers for restrictions and phosphatase. For your Insert in the experimental setting you have provided, I believe you can skip it.