Markos of PTC, his advice years ago was, go for a good barbell, save money on weight plates. And I agree. So don't get the cheapest bar - trust me, you always end up regretting it.
But also consider the kind of rack you've got and its hooks and safeties, if they're just metal then they'll grind up the bars where they hit, which is basically where you grab it for a snatch. If you ever want to do the quick lifts then you'll need a separate barbell for it. If your rack has got hooks with plastic padding then it'll be fine.
One of the basic aspects of barbells is their stiffness. If you want it to be able to hold 200+kg in a lift then the bar has to be stiff, otherwise it bends and wobbles and puts you off, and eventually the bend becomes permanent. It can be made stiffer by alloying it with metals other than iron and carbon, which is expensive, or making it thicker, which is cheap. So the cheap barbells are usually 32mm rather than 28mm - and yes, it does make a difference.
The second aspect is the knurling, the hatching for grip. This can be shallow or deep, and sharp or smooth. Obviously, deep and sharp will lead to a better grip on the bar, but this involves more work in the bar factory so also means extra cost. Thus, the cheaper bars have crappier knurling. We all develop our preferences, and they're often different for different lifts - "this one for bench, that one for deadlift" - but nobody prefers shallow soft knurling.
There are other little aspects like how well the sleeves (spinny bits you put the plates on) fit, and so on, but bar thickness, stiffness and knurling are the major things you'll notice in your first year or two of lifting. You don't need a $1,500 eleiko bar, I just wouldn't get the cheapest one. A good bunch of gear should last you literally decades, so a few hundred bucks here or there is not a big deal viewed with that in mind.
Of course, if you've never had any instruction, you might consider splurging on that, too. The various PTCs are good places for that, but there are lots of black iron gyms around these days, not like a few years ago.