The Ryzen5 1600 would give you a very strong platform for future upgrades, so in that sense, it's a good purchase.
Yes, the 260X will limit it quite a bit - the 1600 can pair with much, much stronger GPUs (up to and including a 1080TI).
If you plan to upgrade your GPU in the relatively near future, then I'd go for the Ryzen5 1600 based on the info you've given.
What CPU do you have currently though?
An alternative, if you want a system that you would be a better 'balance' for the money.... you could look to a Ryzen3 1200 and a 1050TI (+MB & DDR4) Would work out only a little more money than just the 1600 + MB & DDR4 (10-15%)
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