I would like to push back on the idea that you need a huge budget to go after a topical collection. If you want to pick a topic like "pristine examples of the early development of the Rai school," yeah, that's going to be expensive (and I would definitely like to see it). But you can pick other topics that are also interesting, but far less capital-intensive.
For example, you could try to put something together from each of the three major sword-smithing cities in the Edo period (Kyoto, Osaka, and Edo/Tokyo). After that you could expand to cover the other four major regions. Are we talking about an immense fortune to put this collection together? Not necessarily. But it's, I think, more interesting than "here are three blades chosen at random because I got a good deal on them."
That's just my opinion though, and I am just some random person on the Internet! Ultimately, I think the important part is that each collector finds something interesting and significant in the collection process itself, so that they stay engaged with it and keep learning. Whatever fills that niche for you is a good collecting model for you and your collection.