If you are practicing all you need is a power, a guitar and amp and a cable. And its fun just like that. OK a multi makes it more fun but heavy FX will mask your mistakes, so you practice on a clean amp setting. How and where you are going to play, should always be considered before buying new gear. Before I had, what could loosely be called a studio, with everything in place. I used to practice in a spare bedroom. Amp and guitar were brought out of a cupboard, plugged in powered up and away I went. No problem. End of session power off, unplug put away, wash rinse repeat. My first multy was a Zoom GFX 707 around 1999/2000 and I bought it as it had a small footprint and also ran off batteries.
So if the living room is where you are going to play, hump your gear in set up and away you go. Think of a band that’s gigging. Every venue set up then tear down after, on and on.
With the electric guitar, unless you’re playing unplugged you unfortunately probably are kind of stuck playing where your amp is. Alternative is to lug the amp down to the living room or maybe just leave it in there ? That’s what I’d do but I live with my partner so can’t !
Alternative is for you to look into a smaller amp with inbuilt effects that you can carry round the house. These days you can get some very small and light practice amps
I’d also say , if you’re just practicing playing you don’t need all your effects set up, unless of course , you’re practicing using your effects! You wouldn’t set up your complicated gigging setup every time you wanted to have a noodle around unless you’re fortunate enough to have some kind of home studio
Why not get a mustang micro and a pair of headphones for practice, very portable of plenty of flexibility. Plus you can bluetooth from a phone or tablet via the mustang to your headphones so can stream backing tracks or anything you want to play along to.
Not sure why someone would want to regularly change the room they practice in. At least, not often enough to make moving an amp and some pedals a serious annoyance.
But if you really do need mobility, then the answer is either a small amp with effects built in (like the Katana linked above) or an even smaller headphone amp which weighs nothing at all. The Fender Mustang Mini looks particularly good and has more effects than you can shake a stick at. If you want something cheaper, you can get decent ones for £40 or so. My Wife uses a VOX amPlug 2 which is a great bit of kit. Far less options than the Fender, but sounds really good and comes in a variety or styles.
As for wireless systems, you don’t buy them separately. They come in pairs… one plugs into the guitar, the other into the amp. Bought mine on Amazon for £50 and they’re brilliant. I can literally walk all around my flat while playing, should I feel the need to. (Which I generally don’t.)
Lekato 5.8Ghz Wireless Guitar System - 5.8Ghz means less chance of interference. It’s a range supported by most phones and routers these days, but not often used by default. I live in a busy residential estate and have never had any issues.
VOX amPlug 2 Headphone Amp - If you want to hear what all the different models and effects sound like, search YouTube for “AmPlug 2”. One of the top results should be by Music Bliss Malaysia, where there demo everything.
As @goffik says, a headphone type amp works well.
I have my guitar, a Boss Pocket GT ( BOSS - Pocket GT | Guitar Effects Processor) , a 1 meter cable (with right angle connectors) and a set of headphones. Using this setup I can put the Pocket GT in my pocket (imagine that!) and freely walk around playing the guitar (or sit, stand or whatever.) No big heavy equipment, lots of freedom, travels well and doesn’t disturb anyone.
Wow , Just now I discovered I had a iRig2 some where in my room and I just connected my guitar to my ipad with no problem, Garageband and many effects so I canceled VOX amPlug but went ahead with the wireless system that will definitely come in handy