I have USB-3.0 ports on my computer and I need to get an extra HDMI 2.0 port to connect another 4K screen.
I have option to buy USB-3.0 to HDMI connector and it will cost me
around $100.
That sounds about the right price range for a DisplayLink adapter. I haven't used DisplayLink adapters myself but I read good things about them. DisplayLink makes a number of chips for adapting USB to HDMI, DisplayPort, VGA, or whatever. A number of dock and dongle makers use the these same family of chips from DisplayLink and given the reviews it's a good option.
Or
I can by a connector USB-3.0 to USB-3.1 (type-c) for $5 plus another
connector USB-3.1 (type-c) to HDMI for another $10.
If it will work I'll save around $85.
But will it work? Why?
Not likely.
When I read about people with their adapters for their computer I think of my brother with his camper and his adapters. It's a big camper and so it has a 240 volt 50 amp plug for "shore power". But not all camping spots have that kind of plug so he has a shoebox full of power adapters, from a number of 30 amp plugs, a couple 20 amp plugs, and even a common household 15 amp plug. He can adapt this big plug down to a 120 volt 15 amp outlet, like the kind you'd use to plug in a table lamp, but does that mean my brother can run his camper's air conditioner, microwave oven, refrigerator, turn on all the lights, and crank up the stereo with that adapter? Of course not. He has to keep his electrical usage down to 120 volt 15 amp or the circuit breaker trips.
That USB-C adapter still leaves you with the same USB 3.0 capability as the USB-A port it was plugged into. To get video out of it still means needing a $100 DisplayLink video adapter.
P.S.
I'll be happy with a HDMI, DisplayPort or DVI and (2560 × 1600) is
fine, if there would be solution. But (1920 × 1080) - is not enough.
To get HDMI, DVI, DP, or VGA from USB-A means using some kind of DisplayLink chip or something like it. If you have a USB-C port on your computer then that doesn't necessarily open your options much since there are plenty of USB-C ports that lack support for any video output. Those that do support video output on USB-C is nearly certainly DisplayPort (or "DP" for short).
If DP works for you then a cable from your DP capable USB-C port to some DP capable display should be cheap and easy. If you want HDMI then you'll need an active adapter. There are passive adapters that will allow one to plug an DP cable into a HDMI socket, that doesn't mean one will get video. The "full size" DP ports on the backs of computers for years often had that funny looking "DP++" symbol next to it. This meant they supported passive HDMI adapters and cables. Few USB-C ports support HDMI. If you want HDMI from USB then you'll need an active adapter, probably costing about $100.
MHL is another video standard you may come across. It supports 4K screens from MHL capable USB ports using inexpensive passive adapters. It's not very popular though. I'll see MHL/HDMI combination inputs on TVs and monitors but not too many things will output MHL. If you are looking to save money then consider MHL gear might be cheap. Or consider my mention of it merely being more complete in listing your options.
If you haven't already bought that $100 DisplayLink adapter then I expect that is were you will end up. There's a reason they are popular.
