As mentioned by some of the others, there are alot of options and you're not stuck to just one or the other. Having said that I think it really worth thinking about immediate vs long term needs/goals, cost, flexibility and your expectation regarding tone...but also where you plan to use your gear. Like just at home for personal use, jamming with friends, playing gigs, at church, etc.
One option if the immediate goal is to be able to use heaphones is to simply get a small amp that has headphones. I have the Positive Grid spark amp at home that has built in fx, amp model for acoustic, electric and bass and has headphone out....it's also a bluetooth speaker. There are also many different amp/cab simulator pedals that have headphone outs, like the strymon iridium, Walrus ACS1 and a number or others, or as other have mentioned there are a variety of modelers out in the market like the line 6 stuff....but you kind of need to figure out what you need via your signal chain. For example although some amps, modelers, cab sim pedal have an FX loop, many do not, so you need to decided if an fx loop is importation to you. If you're running your amp clean and doing everything with your pedals, it's probaly not as important, but if you're wanting to crank up the preamp to get the overdrive through the amp, or use pedal in front to push the amp harder, but you need time based or modulation fx after the preamps stage, than an fx loop might be more important...
I just got an Walrus ACS1 for when I play at church, so that I can go direct into the board, but I place my time based FX (delays and reverbs) after the ACS1, so if I use the headphone out on the ACS1, I won't hear anything after it, since there's no fx loop. I also used to use Line 6 POD HD 300 in the past, but it didn't have an FX loop, and I found that the signal chain was too limiting. I like to stack overdrives, and sometime stack 2 delay pedals, but this wasn't possible with the HD 300.... That's why I say take the time to figure out first what your need and expectation are first.
Also if you go with something like the JOYO american, keep in mind that this is only the preamp section of the amp and that you don't really get the speaker cabinet emulation part of the amp...just something to think about.
Almost forgot to mention, some of the amp/cab sim pedals while they produce great amp like tones when plugged in direct, have many users that say the that headphone output aren't as clean and can tend to be noisy.