If I were you I would take a water sample to your local pet shop and have them test for your water hardness. Get them to tell you the gH and kH. They will do it for free.
My Honest Opinion: I think you should choose between either the bloodfins or the neons. I think it is better to have one large school than two smaller ones. The fish will be happier for it. Also, keeping a school with less than 5 fish is stressful and a small school of 6 fish would not look that great schooling around. Both for aesthetic purposes and fish health I recommend you pick one species.
How much would the Bolivian Ram cost me? My grandma is buying me these fish and I'm sure she won't want to spend a lot. So if I got 6 cories, one pleco, a ram, some neon and bloodfin tetras about how much would that be?
This is very important because if you don't have the right water, the fish wont be healthy and could die.
Once you find these numbers then we can really tell you if it is a good idea to keep these fish. Please do that before buying the fish.
The Bolivian Ram and the Bristlenose Pleco will cost $6-$8 each
depending on your shop. I've seen them as low as $4 before.
Cory's and Neons cost between $1 each to $3 depending on sales.
DO NOT BUY A COMMON PLECO - Attains anywhere from 12 to 20 inches. TOO big.
Before getting the fish you want to set the tank up and cycle it. Excluding the neons, these are all more fragile fish that cannot handle a cycle and WILL die if you try to do an fish in cycle.
I don't know how much experience you have in this.
You can seed the new tank with bacteria in the gravel of an already established tank (your betta tanks). Once the tank is cycled and you have everything stabled I would go get All 6 corys to put in the tank. DO NOT get all the fish at once or it will shock the system and you will loose fish.
Live plants help this process by soaking up ammonia and other nitrogens.
Once you add the cory, wait a week and test your water to make sure ammonia and nitrite are at 0.
IF levels are stable you can go back and get a bristlenose pleco and the 6 neons. I would only get 6 neons at a time so as to not shock the system.
Wait a week. Get the other 6 neons.
Wait another week and then go back to get the Bolivian Ram.
Each week I would also add more and more plants to the tank (this is assuming you have a local fish store). The plants are very beneficial. Something like Java Fern is low light and grow slow so you wont have to care for it much. It looks beautiful too.
This will be your idea tank:
I hope I didn't give too much info at once but I would really find out more about your water before doing anything about your fish. I would also make sure the tank is cycled before doing anything.
Once everything settles down and if you do get plants....later on down the road you could add maybe 2 more neon tetras or a cory or something.
It is always good to keep stocking levels low while establishing a tank. Especially for the safety and health of the fish.
Do you have a test kit?
API Master Test kit is very reliable. Water based test kits over strips.
Hope this wasn't overwhelming. I'm just trying to make sure you take it slow and consider your water before getting the fish.
Let me know what your LFS says about the water. Once you have given these parameters I can better help you find the right species of cories, tetras and other fish for your water if they aren't suited for these.