.003 main clearance doesn't really have that much to do with automatically qualifying you for 20W50 oil. Its all about load, and rotating speed vs area of the bearing. When one dives off into studying such things, you quickly discover a few constants surrounding a boundary layer... to condense, .003 will be just fine - even if you ran 30 weight... You will also find, that most aftermarket builders go a little crazy with oil pressure. Google the API standards for supplied oil pressure requirements to industrial equipment - you'll be shocked. In your case, with a hydraulic camshaft, the extra pressure is welcomed - in my opinion. And finally... depending on what your rods side clearanced at, making sure you have a handle on "oil control" might be a more worthwhile pursuit when considering your bearing clearance, than viscosity.
For break in, I suggest you use whatever gives you peace of mind. Most have suggested "extra insurance" type oils - that's a hard concept to argue. I spend more money than I want to when it comes to this part, if that helps you any.
For long term oil, if a quality oil at a good price interests you... Delo 15w40 would probably suit you well. I have access to the oil analysis lab in the reliability shop, where I work... Delo is awfully good stuff for the price. NOT saying its the best oil, the only oil, or that you shouldn't run Penn, Gibbs, or VR1 etc - just saying, it's a cost effective option that I have confidence in. I run it in darn near everything I own, have been for years. If you notice, it is one of the only mainstream manufacturers that sells their oil in sealed containers as well... that's usually a pretty good clue.
Without typing a full blown novel - one other thought to share. You absolutely do not need synthetic oil. You can buy it if you want it, but it won't do anything for you that a conventional wouldn't *in this application*. Now, if you had .001 on the mains and were turning 8000, that'd be a different story.
Good luck with your new motor, hope all goes well!