@Derek Hebert as far as waiting for better rates, predicting interest rate movements is a notoriously tricky business and even the pros (who have a lot more money on the line) get it wrong. I would only look at "today" interest rates and see if the #s make sense for you with those rates.
As far as when to refi, I guess it depends on what you think the value is now (what you think you can get out of the property from the refi) vs. your cost to refi.
Remember that the rate on a cash-out refi is going to be a little higher than your initial purchase loan so be sure to take that into account when you're figuring out your new payment amount. It may also be tougher to refi if your purchase loan isn't very "seasoned" (hasn't had a year of on time payments for example).
It is possible to refi with no/lower closing costs than usual, but just like good real estate deals, you have to hunt around for those. Sometimes you can get a good deal if you approach a bank or credit union you already have a relationship with. You can also ask multiple mortgage brokers too of course, about their loan programs.
Be careful with the #s though. The first time home buyer loan is pretty attractive, so you may not get as good of a deal on your cash-out refi and you don't want your 500-600 cash flow to turn into 100 cash flow. You want to pay particular attention to your new debt service coverage ratio - i.e., how much of a margin you'll have between your net income and your mortgage payment.
Generally, I recommend people hold a property at least a year before refinancing, so they get really familiar with all the ins and outs (and upcoming expenses) of the property. You also want to turn your "plan to be making" cash flow into "actually making" to be sure it's what you're expecting.
I don't have personal experience with a 203(k) so I'll have to defer to others on that. I know you'll have to get written estimates from contractors for the repairs and that those repairs will be paid for in draws as each phase of the project is completed (a little at a time, not all at once). My general thought is, it's more leverage, so just make sure that the higher loan amount isn't going to make your loan payment so high that you're skating on thin ice (again, debt service coverage ratio).
Also AFAIK the 203(k) is for owner-occupants, so my guess is you'll have had to refi out your first-time homeowner loan on your current 2-family, before getting a 203(k) on another property. Otherwise the loan officer / underwriter is likely to say, wait, this other loan was for an owner occupied property, but this 203(k) is for owner occupied - which one are you really living in? You may also have agreed to live in the 2-family for a certain # of years before moving out for example (check your loan terms). And if you refi the first time homeowner loan with an investor loan (not owner occupied) which is also cash-out, that'll be an even higher rate.
I know this may be heresy in a rising market, and particularly regarding the BRRRR strategy, but be careful about leveraging yourself (your properties) too much. Years ago in a seminar the guru-at-the-time called that a "house of cards" and the phrase stuck with me. Remember, leverage is a powerful sword but it cuts both ways too.