Wordpress change theme on live website - how and consequences

I've decided to change my WP theme but my website is live and has some traffic on it.
The problem is I've designed everything (images dimension, posts designs, widgets, sidebar) for my currently theme to looks unique but I've highly doubt it will look the same on my new theme.
I don't want to upload it and changes things until I've got what I want as may take some time and my website will look like shit while I do this.

So how can I makes changes to my new theme that has no effects on the current site and after all is done to publish it? That means I need to see how each posts will look with the new theme, changes things, save the changes and move on next. Save everything and when all is done publish.

And what could be the consequences from SEO point of view?

There are few ways of doing this but the easiest one that you should go with is by using the following plugin: https://wordpress.org/plugins/theme-switcha/. Once you go live with your new theme, your website SEO score could improve but it can also go down the hill (loading speed, additional file requests, etc...). Talking from experience, the impact won't be big if you don't actually change the whole structure of the website while changing the theme.

man too bad you aren’t with a host that has staging. maybe you can export your site and import it to a fresh install and test it from there.

The best approach is to:

1. Take a backup of your site. There are few good free plugins out there like : All-in-One WP Migration and Duplicator.

2. Install the site on your local computer. You will need to install XAMP/LAMP or WAMP based on your operating system.

3. Make all the changes you want on the localhost.

4. Once done, take a backup again but this time of localhost an push it to the live server.

I hope it answers your question.

Ok, does not sounds that complicated.
I think I will make the changes on my local server and upload it live once is done.
Thank you all!

This depends entirely on how much your existing theme is actually doing to power features of your website. Is it a base theme? A child theme? The more logic in functions.php that's vital to your own site, the more work you'll need to take to port over functionality to have your new theme support various custom features.

It's a little hard without seeing a side-by-side to know what is involved, but anything can be done.