I had a temperature problem with a Barista Express but it was only noticeable if I made and tasted 3 drinks on the trot. More of a strength of the brew than a taste variation. The 2nd and 3rd were the fine. Cured by preheating. My way but another suggestion is to run a little bit of steam before pulling the actual shot. Flavours mentioned for beans could reproduced probably without the preheat.
Totally different a Piccino. Temp control not good. A rather different taste of coffee comes out but still a decent drink. ;) I aught to check it over carefully and sell it. It will steam milk but rather slowly and temp stability on steam probably isn’t good.
Gaggia is very popular but many buyers seem to modify them rather quickly including adding PID.
All Sage machines give at least reasonable temp stability. The penalty is the need to keep an eye on descaling.
My way of preheating was pretty simple. A 2nd portafilter with an empty dual wall filter basket in it. Just run a part shot through that. Flow rates will be in the range the PID is intended to work at. I bought a used one to convert to bottomless. These can be bought now.
Grinders - a rabbit hole. What ever some one buys other options for specific reasons are likely to be mentioned. Never seen any suggestions about changing from an EK47s.