I currently have Record, Veritas (Lee Valley) and Lie Neilsen planes. The biggest differences between them are the precision of adjustment and their edge holding ability. The Veritas is much better in both regards than the Record and is easily worth the difference in price. It can also be used right out of the box with minimal honing of the blade. I found that Records require extensive tuning. Overall, I'd say the Veritas is the best value in a block plane on the market. Lie-Nielsen planes are exquisite pieces of workmanship, but functionally, they aren't appreciably better than the Veritas products. The difference in price is hard to justify, unless you just really like fine tools.

For sharpening, use whatever method your prefer (stones, diamond hones or sandpa per on glass) for roughing in the blade, but I'd suggest a 4000 or 6000 grit waterstone for finishing. The finely polished edge they produce really does last longer, especially on the harder blades of better planes. I'd also recommend using a honing guide. If you buy the Veritas plane, get their honing guide, too, as it works best with on the tapered blade in their plane. It also works well with other plane's rectangular blades, but there are cheaper jigs that will do the job.