askchapo

Just grab a cheap current gen smartphone or a second hand smartphone and only install those apps?

You might need to flash a custom rom to delete certain apps that come pre-installed and you might want to find the right launcher so you can customise your app drawer to throw a few apps necessary for installation or handling links (e.g. when you get the inevitable hyperlink via Signal that you need to be able to browse) into the oubliette so that you only have a dialler, SMS, Signal and Telegram visible.

Install only what you want and have someone you know lock down the ability to install anything else. Should be possible with parental controls

You want a dumbphone - of which your options are going to be like phones that specifically lack browsing/internet features like Tracphones or Nokia phones. (Another alternative is like the Sunbeam F1 or various Japanese dumbphones)

Alternatively, you could just buy a cheap Android phone and use ADB to remove those features (like the built-in browser and wifi) you don't want.

link but the subreddit for dumbphones is an excellent resource: https://old.reddit.com/r/dumbphones/comments/zpw77o/state_of_the_dumbphone_2023_read_this_first/

You cannot have signal and telegram but also no web browser or anything else.

First you're looking at flashing a phone with a stripped down custom android OS like lineage but even those come with a browser installed as a bare minimum of functionality. Then your looking at side loading those two apps without installing google play services, which you might be able to do with telegram, but not with signal. IIRC signal requires google play services installed. You can try to flash the pico version of google but I think you dont want to go that far.

You may be able to get telegram working on a KaiOS flip phone, but those can actually access the internet as well (very shitty, has huge 2004 RAZR web browser energy). Signal does not and will not ever have a presence on KaiOS unless someone with very very deep pockets decides to throw absurd money at the signal maintainers with the specific demand that they create and maintain an official KaiOS store webapp because of the way that KaiOS works.

If you want to escape app hell, maybe try a Pine phone and run an open source OS on it. It probably won't stop you from accessing the internet, though.

Might be easier to give advice if you can explain the motivation. Are you worried about privacy with smartphones? The cost? Spending too much time dicking around on it? Controlling a kid?

I don't know of a way to get a phone that only has those apps, they require internet to work. GrapheneOS can be quite secure and you can simply not install any more than the base apps and then freeze the built in browser, but then you'll need to manually update Signal and Telegram and I assume you needing to unfreeze your browser to grab regular updates is far too much of a pain. Running outdated versions of secure chat apps is a risk.

A colleague of mine is happy with their phone from Punkt.