Aided Phone or Video Calls
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Whilst unaided video or voice calls that are automatically answered have many advantages, if your loved one is in a care or nursing home then the carers should be able to assist with calls to a mobile/cell phone that you provide for your loved one. Voice calls don't require an internet connection, nor as much set up in the first place, and a non-smart mobile/cell phone for voice calls is very cheap to buy (or you may have an old mobile/cell phone that could be used, having deleted contacts, texts etc).
The carers will need to keep the phone where they can answer it, and keep it charged up. Check with them the best times of day to phone (generally avoid meal times and other busy times).
Suitable phones and SIM cards
If necessary seek advice from a good mobile/cell phone retailer regarding a suitable phone and a suitable SIM card and the costs involved.
Choose a phone network with a good signal at the home. One option would be for your loved one's phone to use a pay-as-you-go SIM with just a small top-up, and then you call from a (mobile/cell) phone with an 'unlimited' call plan (but note that there is a limit in reality). For your loved one to make a call to you, the carer can always call you and then you call back so that you're still using your 'unlimited' call plan.
However you arrange it, make sure that your loved one's phone can't rack up unlimited bills (noting that any spend cap may have a delay during which the cap may be exceeded unnoticed). Also remember that calling from a landline to a mobile/cell phone is usually very expensive, so you'll probably be best to use a mobile/cell phone too.
Headset with microphone
For aided calls we'd recommend your loved one using a headset with a built-in microphone, to avoid problems with the phone's speaker or microphone drifting away from their ear or mouth, or the phone being dropped.
An over-ear one is likely to stay on better than an earpiece type, but needs to be put over the ears correctly for comfort.
Wired headsets avoid the problems of bluetooth ones, which need charging (in addition to the phone being bluetooth capable and the headset being paired to the phone via its settings). Make sure you get one that's suitable for your phone, together with any adapters required.
Headsets now mostly come with the microphone on a stick in front of you, which might be distracting for some people, but if you get one that can be swivelled down a little it should still pick up sound well enough (older headsets had the microphone in the cable, and they worked ok).
Aided video calls
Aided video calls, with the carer having to answer the call for your loved one, can be made over the internet using a mobile/cell smartphone or computer in a similar way to unaided ones that are automatically answered but which require an Amazon Echo Show device. The same considerations apply to internet connections and data costs.
There are many popular software apps for video calls, such as Zoom; Microsoft Teams and the older Skype offering; Google Meet; and Apple FaceTime (which is only for Apple devices). There may be restrictions on the length or frequency of free calls using these apps.