Gunna be a party pooper and agree with Mr Peepers. I would establish a good relationship with your cockatiels and your budgies first, get them into better housing situations so you no longer have the issues you've been having with them and enjoy them for what they are. Time and patience with birds can really pay off and you could end up with some very fun little companions. I will also say that no bird is cheap. You could find a bird free to good home but to provide them with the best diet possible, enrichment and vets should they be needed it will all add up. I won't say how much I've spent a few times at the vets but it's been enough to not let me allow me buy food for myself for a few weeks. You had mentioned in a previous thread a cat being hit by a car not being treated by a vet due to financial reasons and that may be a good enough reason not to get another bird any time soon. I've been there and done that, got birds when I shouldn't have and have ended up with numerous issues (namely psittacosis). It just isn't worth it sometimes and it's not fair on the bird
That being said! I CAN offer you some advice regarding the species you've listed
Kakarikis (assuming red fronted?) are one of my favoured species. Guessing that you're from the US you may not be able to find them very easily at all. There are a lot of breeders here in the UK and I'm one of them. They are not a popular species at all in the US. They are very energetic and VERY fast. They get into absolutely everything they possibly can do. They don't scream at all and make very pleasant sounds. They are not cuddly birds. They like to bounce on you every now and then but as fast as they hop on they hop off just as quick
I adore them. They're really interesting and unique. They are really messy, which a lot of people don't like. They scratch at their food like a chicken and do everything with their feet. They also spend a lot of time on the ground being a species from New Zealand. That isn't always ideal in a house where there are other animals as the risk of them getting hurt is considerably higher than other species. Not to mention these guys are fearless
This video shows you the noise level and how they are constantly on the go -
With lovebirds I namely recommend the eye-ring species as companion parrots as the peach faced and others can be highly strung and stroppy. I recommend looking into masked, Fischer's or the rarer black cheeked. I have four species of lovebirds and I find that the black cheeked are the sweetest little things. Easy to mix up with black masked but much smaller and that little bit more gentle. Lovebirds can have quite a shrill call compared to some birds and it can be quite annoying. With all of mine together it can get annoying but I just ignore them now. They're in an aviary so I don't have to pay attention to it aha. I'll pop some videos in of those 3 species and the noise level of their calls. They are very short and sharp but they have a trill to them
Black masked -
Black cheeked -
Linnies are ideal small birds but I personally feel that they do better in pairs. The same could be said about all birds but these guys seem to thrive off it even as companion parrots. They're relatively quiet and have an unusual and somewhat soft call like a kakariki. They are slow moving and very deliberate in their actions. They're passive birds and can be quite cuddly compared to lovebirds and kakarikis. They like a head tickle. They also seem to prefer to hang out on you and not sit on your hand... I can't explain it. Like they want to tuck themselves away somewhere on you but are hand shy haha? They do like to burrow. Again an issue to watch out for having multiple pets!
I just LOVE the noises they make. You can see what I mean about how slow moving they are here -
Indian ringnecks. Where to start. In my opinion, they don't make good companion parrots. There are the odd hand raised birds that can be fantastic companions but most IRN are not like that. Don't let the cute YouTube videos fool you. I own this species myself and I can honestly say they can be very head strong, quite aggressive (they also bluff and lunge a LOT) and I think their call is just terrible
I adore them. I think they're beautiful birds. I would just rather not have them as a companion bird. We have wild flocks in the UK and you can hear them coming from far away even if it's just an individual bird. They're intelligent. Destructive. Loud. Did I say loud? Very loud. I had one IRN that was almost silent, another that was normal and my most recent that screams on sight! Every time. She doesn't stop either. Nothing you do makes her stop. I've tried negative reenforcement (ie leaving the room) and I've tried to soothe her but she just screams and screams and screams. I dread to think what she will be like when she gets a boyfriend haha!
Like this... constantly...
Now I'm fine with all bird noises, I can have a cockatoo screaming on my shoulder and not bat an eyelid. But that screechy ringneck shout makes my teeth hurt
Quakers. Cute, floofy, sassy and rather bitey little things if I do say so myself. And if you don't want screaming, they're off the menu
Just listen to this -
I don't need to say anything else about them. I love them. But you won't if you can't tolerate the noise level
I may say things about these birds that just seem negatives but I don't think it's worth bigging them up for people to be disappointed with the birds they have got. I love all species, especially the birds you've listed