I have been mining with 1 GPU for about two months and it's profitable when I crunch the numbers, about a whopping $8 - $9 a month.
Best advice I can give you is think long term; it's a slow grind. Now's not the time to invest any money into it. I already had a gaming PC with a GTX 1060 6 Gig card that I barely use so it's just the cost of electricity for me. Find a coin you like and mine it; plan on holding it for several months or longer and hopefully the value will go up and you can make some $$$.
This is probably the best strategy to earn something with one GPU. Mine new coins with low difficulty and hope they would be worth something in the long run.
I very much agree with this. My experience with RVN has borne that out. Each week when I did my research for ICO's I would look at a lot of coins/releases (not all ICO's - RVN wasn't), and a few months ago I came across RVN and pointed a 3-card (1070 TI) at it and was lucky enough to be getting hundreds of coins per hour. This didn't last too long, but I was able to amass a halfway-decent number of them, which I will hold onto because I happen to believe in the coin itself and the community around it.
And this could definitely be a strategy. Examine every new announcement in the ALT thread, plus look around elsewhere (Twitter is where RVN was actually announced in October of 2017 - I wish I had been paying attention then!) and then point your card/rig at it early and see what happens. When it starts to fall off, find another one. Doing it this way spreads the potential around a bit, such that if, say, 20% of the coins you mine over a given year go somewhere, then those 20% might be worth it. If you stick to just one, then there's much less chance of getting a decent ROI.
Anyway, that's one approach. I'm sure there are plenty of others.