What do you mean by the spoke pattern being "nicer"?
You need to work out the dimensions of your hub - the diameter of the hub flange measured spokehole to spokehole on opposite sides of the flange, and the distance of each flange from the centreline of the hub. You also need to know the effective rim diameter of your Alex rim - easier to look up than try and measure.
You can then use a spoke length calculator such as that at DTSwiss.com to work out what spoke length you need.
Have a good read of Sheldon Brown's pages on wheelbuilding or, better still, get Roger Musson's ebook from wheelpro.co.uk.
If you're struggling post the exact model of hub and rim and spoke count and I'll try and help.
<Edit> You need the same number of spoke holes in the rim and hub - don't leave gaps! It's also a really good idea fr a first wheelbuilding foray to use new components, they build up more easily!