This Onkyo system may be better then many mass market HTIB (Home Thearter in a box) solutions but it is still not going to give you very good sound compared to proper high quality speakers. Better speakers will cost a bit more and small speakers are a bit of a compromise. DVD's do not support Atmos content and this is only available on some newer Blu-Ray disks so I wouldn't worry to much about it unless you want to go down this road. Note even if all your library is DVD it is still a good idea to at least get a cheap Blu-Ray player as these play DVD's really well and give you the option to play Blu-Ray's as well. There are some high end players like Oppo that cost a lot more but have extra video processing features that can improve the video quality of DVD's a bit. A second hand Oppo player may be an option.
As to TV and 4k I would say it will probably not make a big difference unless you are sitting very close or have a really big screen. If it doesn't fill up a lot of your field of vision like in a movie theater then 4k is mostly pointless. The only other advantage 4k has right now is HDR on the latest models and this requires native HDR content which is rare at this stage. How successful HDR is going to be is still a bit up in the air at this early stage. To work out what screen you need to first measure how far from the screen your planned seating will be. From this you can work out the required diagonal size of screen you will need to view SD/HD/FHD/4k resolutions and then you can pick a screen in your budget that works for you.
Here is a good guide for TV size:
http://www.audioholics.com/hdtv-formats/how-to-find-the-right-size-tv
Also as to your rear speakers you asked about I would look into a 5.1 setup at first as this does not require 'Rear' speakers and generally works well for most people. There is not a lot of content going to the surround back speakers but the Surround speakers which are placed to the sides just behind the main seating position are important.
As to your choice of Onkyo they make some ok units and hopefully they have solved the overheating HDMI board problem from their previous generations now. The only big downside right now is they have given up on using decent room EQ systems and implemented their own low quality budget room EQ system instead. If adjusting the sound to fix problems in a non ideal room is important to you then look into Denon/Marantz or Yamaha. Also if you don't care about 4k,HDR and Atmos then a second hand or refurbished or previous years old stock AVR may give you a better deal for your money.
And finally about aesthetics there are a few options. One thing to remember is that a basement home theater is a dedicated space and unlike a living room which has to look decent for living and entertaining etc the basement often has a lot more freedom to add functional objects like speakers that might not work in the rest of the house. People often accept functional but ugly things like exercise equipment in a basement so why not speakers? Many speakers also have nice looking finishes and can add to the looks of a room but be aware that speakers with both looks and sound quality can also add to the cost a bit.