There's a lot of detail to consider. We see all too often someone posting up who bought something based on let's say poor assumptions and not working out as envisioned. Much better to flesh it out and understand the differences/trade-offs with the myriad gear out there. Lots of glorified sales type info about gear as well as downright snakeoil to make it even more confusing. Can take a while to sift thru. Throwing money at things isn't necessarily a good thing in audio, tho, you can do quite well with a modest budget.
I remember when NuForce made a splash, think they put out some decent solid gear at a good price....IIRC Optoma bought them and haven't heard much about them since. Monitor Audio makes some very nice speakers, but like many things, depends on model and the suitability of the model to your needs. The MA speakers you mentioned are small bookshelf models and really should be supported by a sub IMO. You might not be a bassoholic like myself and could live without....YMMV. Generally takes a much larger speaker (no replacement for displacement as they say) to provide deeper bass in appreciable quantities without a subwoofer and often fairly expensive to boot. Whether you need appreciable quantities is another matter, I like being able to altho I limit the spl (sound pressure level) generally these days. I do like gear that helps integrate subs, tho....and much two ch gear does not.
With an amp you still need a pre-amp in that amp alone is generally taken for a power amp. An integrated amp is a pre-amp and amp in one box. A receiver adds other functionality, originally radio tuner, but now often more digital/internet based integration.
In the area of active speakers my only experience is with a pair of JBL LSR305s I got for I think $180 the pair or so and based on generally good comments and measurements. I quite like them and think would be quite a bit better than the Audioengine models you have. I run them off an old 2ch pre-amp so I can use a few different sources with them, an Audio Chromecast to stream to, and an optical disc player. There is a little bit of hiss I can hear if nothing is playing if I sit close to the speakers, but not how I use them in that room, more like 5 ft away and think they're fairly terrific in that small room (a bit shy of 13 x 10). Somewhat comes with active speakers to a degree but if not on your desk there are some terrific choices out there, some like Shady mentioned in the other thread (he's our speaker reviewer btw). I've even used just the Audio Chromecast unit with the speakers directly....a bit funky with a volume control on each speaker but they're indented positions for volume so not bad to set up identically. I can stream to the Audio Chromecast unit from my phone or computer.
Would you like to have other than modern streaming convenience? Digital sources only? Want to use a disc player? Turntable?