On stays, you might as well do it through Marriott. Yes, Hilton is good for treating you on redemptions, but you can get much of that simply by signing up for the Citi Hilton HHonors Reserve card which is $95/year (no first-year waive) but instantly makes you Gold (mid-level at Hilton). And then from another Citi card (that's actually chunrable) you can get 50k HHonors points each time.

Marriott status, OTOH, is not easy to get other than through stays. So that's where it makes sense putting your stays, as you don't need stays to get good HHonors status.

Then you can have Marriott status (you want at least Gold, which is 50 nights a year, or 35 nights if you get and hold the Marriott Premier credit card from Chase) plus HHonors status.

Then use up your IHG points when you go to smaller cities where there's no high-tier hotels anyway (smaller cities often have only Holiday Inn Express in IHG and Hampton Inn in HHonors and Fairfield Inn in Marriott Rewards, and all of those give everyone everything free anyway, so there's not a huge difference between having status and not having status at those properties usually).