I would add that it also depends somewhat on what condition you generally keep your bore in. For instance, some shooters have actually cleaned after every shot--they're going to notice a difference pretty quickly, because a perfectly clean bore is their benchmark for consistency. I clean pretty regularly, and generally notice groups opening up a little on the Savage around 200 or 250. I think most guys fall in between that and ~500 or so.
To be frank, cleaning schedules one of those things that most people overthink. Just shoot. Clean it every few boxes. I think it's more important to really clean it when you do, not how often you do. I prefer to use dedicated carbon and copper removers from the same brand to avoid chemical interactions. Montana Gold and Bore Tech have both been good to me. I brush and patch for carbon, then copper, alternating until the copper patches stop reacting. This is because it's quite common to have carbon and copper deposits layered in the bore. I'd also add that I find cleaning rod selection to be important--I find coated steel just fine, but I absolutely won't use any cleaning rod with a brass female end--it reacts with your copper remover, giving you false positives and leading to corrosion that seizes up your cleaning jags (which incidentally, should also be non-brass, I like Bore Tech's Proof Positive jags).
I'm currently using a Tipton, only because I've been too lazy to find a replacement. It works pretty good on the .223, but it's complete garbage on the 6.5CM. If I were to pick, I'd go between a Lucas, a Possum Hollow, and a Sinclair, in that order. Having to get caliber/chamber-specific attachments is a pain, but it beats a bore guide that doesn't seal.