That doesn't sound like a lot, that's a hit every couple of seconds.
It depends on how complicated your website is, in some cases what technology you're using in combination with the size of your server you're renting, and if it's 1,500 in the first second or 25 a second. Either way, load tests for your site would be good for you.
There's no good excuse for ANY website or platform these days to not be able to handle this amount of traffic with absolute minimal effort. In fact, handling 10x more should be trivial (and cheap).
Well if you're ultra cheap like me, you'll have to think deeply about scaling up your $5 instance lol
There are a lot of factors that go into site performance. Knowing your site can handle what other people have seen is a good start.
Or you can design it to be light and fast from day 1. I had no trouble with the same level of traffic during a ShowHN on a $5 droplet.
You can design it to be light and fast, but you wouldn't know unless you test it right? Good to know that a cheap droplet can at least handle rendering the landing page though.