Hi Rob, read
this article explaining oil viscosity & the like. It will give you a greater understanding, and help you to make an informed decision.
I would go for a high-quality, fully synthetic oil personally; as your engine is modified & it will give you the best performance/protection. Although typically, it is a bit dearer than semi-synth.
The best way of finding out which oil grade is best for your engine is to just try a few. Really, your 5 options are;
0w30
0w40
5w30
5w40
10w40
I am going to be bold & say that any of these grades will work fine in your engine without any issues, but some might be better than others. (Some may disagree with this).
The '0w' varieties are for ultimate protection in cold-start conditions; so ideal for winter, or just fine for the rest of the time. Not really necessary in this country though imo. It's not consistently cold enough.
10w40 is a good all-rounder. Arguably the most widely used of the oils, and works well in most average petrol engines. You won't go too far wrong with 10w40.
Then there's 5w30 or 5w40.. This is where I'd be looking if I had your engine. And will indeed be where I will be looking, when I get my 2.2 engine fitted in March/April.
5w40 - Gives good cold-start protection, and excellent protection at higher temperatures because it stays more viscous (thicker). However, it may reduce engine performance ever so slightly, because higher viscosity creates more drag (although you might struggle to notice the difference). This oil will be ideal if you want an easy life, and don't change your oil that frequently.
5w30 - Gives good cold-start protection, and also superb protection at higher temperatures, but you
may find it burns off/wears out a bit quicker; because it's thinner. However, engine performance is maximised.
The only problem with '30' grade oil, is that because it's thinner, on high mileage or worn engines, you may get a bit of seepage through the piston rings; causing it to burn off faster & your exhaust to smoke a bit. However, this shouldn't be an issue in your case because the engine was rebuilt not so long ago & should be in tip-top condition.
So the choice of oil grade really depends on how rigorously you will
realistically be maintaining/servicing your engine.
Imo, if you want decent, easy motoring; get 5w40. If you want slightly more refined motoring & don't mind opening the bonnet a bit more often to top up, get 5w30.
This is just my opinion though. And you may well find the '30' doesn't burn any quicker at all. It really depends on the condition of the engine. But it won't hurt to try.
You will more than likely find 5w40 is a bit cheaper to buy than 5w30.
In terms of which brand...who knows.
Some say Mobil1, some say Amsoil, some say Honda..and some even say other things. None, or any of these may be correct.
My choice would be Mobil1 or Shell Helix Ultra personally. Or whichever is on offer somewhere. Or
Motul 300v ftw.
Decide on what grade you want to try first, then look for a deal. If you need a hand finding something, or you want people's opinions on something you've found, post up.
Probably best to invest in 5 litres so you've got enough for the oil change, as well as a bit to top up.
Hope that helps, or confuses you.
) and got my manager to call up euros and order me oil, filter and plugs whilst i was on a job for my B20a1 2g. I wrote that i wanted 5-40 either castrol or mobile oil as I've read on here that either 10-40 or 5-40 will be best (as the engines been modded n that and i only want to use the best) 
