Wireless is a silliness factor really. It's not bad, in theory, it's horrendous in reality. Run wires and save yourself SERIOUS headache.
You can't 'paste' a screen to a wall, but you can buy a fixed frame screen of very good quality for not a lot of money and hang it from a single (or two) small nails like a photo. You can also set it on a shelf to hold the screen up, or build a very simple stand for the screen out of 2x4s for around 10 bucks. Seriously, easy solutions for higher quality.
But, facts be facts...
How big is your room? Width of the projection wall and distance of the room front to back?
Where do you plan to set the projector? High on a shelf at the back of the room? On a low shelf between seats at the back of the room? In front of where you sit? Where would you like it and where can you realistically put it if you have some flexibility in placement?
That said: You can use a Roku streaming stick and stream content from online to the projector with the Roku plugged in directly. You can also plug your phone or ANY video device into the projector directly, but audio may still be an issue.
For a bright solid 1080p image, the Viewsonic Pro7827HD is a very good entry level product at about $500 for the projector. It has audio out if you must use a sound bar, or you can pick up an actual surround sound system from $250...https://www.accessories4less.com/make-a-store/item/onkhts3900/onkyo-ht-s3900-5.1-channel-home-theater-receiver/speaker-package/1.html
Be aware that even if you can't do the full 5.1 audio setup, you can set it up with 3 front speakers and the subwoofer and get MUCH better audio than any speaker bar can hope to deliver. That's real bang for the buck!
So, we are at about $750 so far.
Add about $200 for a quality screen that will last you for years. These start at about 92" diagonal...https://www.amazon.com/STR-169120-Silver-Ticket-120-Diagonal/dp/B00DGVHZSA/ref=sr_1_1_sspa?ie=UTF8&qid=1537556166&sr=8-1-spons&keywords=silver%2Bticket%2Bprojector%2Bscreen&th=1
Add a Roku streaming stick for $50 and plug in your cable box and your game system and enjoy the heck out of everything for right around $1,000 total.
If you want to go the super easy route, keep the screen, ditch all the speaker stuff and the rest and use a XGimi H1. I would recommend the H2, but they aren't yet fully configured for USA use, so mostly Chinese menus. They have built in speakers that sound decent (not great) and Android OS. Plenty bright enough for a 100" screen or smaller.
- Theater, whole house audio, and technology consultation during the build and installation process in the Washington, DC metropolitan area.