Can MacBook 2018 output to a 4k external display?
Q1: Can a MacBook Pro 2018 output 4K?
Apple has a technical specifications page for almost every product they sell burried in their knowledge base.
This is the one for your computer, it states:

Video Support
Simultaneously supports full native resolution on the built-in display at millions of colors and:

Up to two displays with 5120-by-2880 resolution at 60Hz at over a billion colors
Up to four displays with 4096-by-2304 resolution at 60Hz at over a billion colors


So yes your computer can output consumer 4K (UHD/Quad HD/2160p) 3840x2160, but also  4096×2160 (DCI 4K) on up to 4 displays at once.
There will be performance limitations when running like this.
Q2: What options are there?
There are a wide range of monitors on the market it would be impossible to really answer this, sites like YouTube provide a broad range of reviews for displays, I have one in mind that I would recommend but don't feel it approriate to do so on this type of website.
Q3: What kind of budget am I looking at?
This is also hard to address as prices in your country will be different from mine, but 4K monitors are very affordable now, however stick to known brands and be careful to ensure you get ones with modern connectivity like USB-C which are going to work well with your laptop, and that possibly having charging integrated.