[SalesForce] Display Radio buttons group in visualforce page

You can try this

Apex Class :

public String SelectedRecordType {get ;set;}
public List<selectOption> getRecordTypes()
{
    List<selectOption> rTypes = new List<selectOption>();    
    for (RecordType  a : 
            [Select Id, Name,DeveloperName FROM RecordType 
            where SobjectType = 'Your_Custom_Object_Name__c']) 
            {
                rTypes.add(new selectOption(a.Id, a.DeveloperName ));
            }
    return rTypes; 
}

Visualforce Page :

<apex:PageBlockSection> 
                    <apex:PageBlockSectionItem >    
                        <apex:outputLabel value="Record Types:" for="Types"/>              
                        <apex:selectRadio value="{!SelectedRecordType}" id="rTypes" layout="pageDirection" style="margin-top:-10px;margin-left:-18px">
                            <apex:selectOptions value="{!RecordTypes}"> </apex:selectOptions>
                        </apex:selectRadio>
                    </apex:PageBlockSectionItem>
</apex:PageBlockSection>

You can use and rerender attribute to render Tables accordingly.

It is ESSENTIAL to request RecordTypes by DeveloperName please Check here.

You can use wrapper class here. This is the best option in your use case. I am adding some sample code taken from Salesforce docs.

public class wrapperClassController {
//Our collection of the class/wrapper objects cContact 
public List<cContact> contactList {get; set;}

//This method uses a simple SOQL query to return a List of Contacts
public List<cContact> getContacts() {
    if(contactList == null) {
        contactList = new List<cContact>();
        for(Contact c: [select Id, Name, Email, Phone from Contact limit 10]) {
            // As each contact is processed we create a new cContact object and add it to the contactList
            contactList.add(new cContact(c));
        }
    }
    return contactList;
}


public PageReference processSelected() {

            //We create a new list of Contacts that we be populated only with Contacts if they are selected
    List<Contact> selectedContacts = new List<Contact>();

    //We will cycle through our list of cContacts and will check to see if the selected property is set to true, if it is we add the Contact to the selectedContacts list
    for(cContact cCon: getContacts()) {
        if(cCon.selected == true) {
            selectedContacts.add(cCon.con);
        }
    }

    // Now we have our list of selected contacts and can perform any type of logic we want, sending emails, updating a field on the Contact, etc
    System.debug('These are the selected Contacts...');
    for(Contact con: selectedContacts) {
        system.debug(con);
    }
    contactList=null; // we need this line if we performed a write operation  because getContacts gets a fresh list now
    return null;
}


// This is our wrapper/container class. A container class is a class, a data structure, or an abstract data type whose instances are collections of other objects. In this example a wrapper class contains both the standard salesforce object Contact and a Boolean value
public class cContact {
    public Contact con {get; set;}
    public Boolean selected {get; set;}

    //This is the contructor method. When we create a new cContact object we pass a Contact that is set to the con property. We also set the selected value to false
    public cContact(Contact c) {
        con = c;
        selected = false;
    }


   }
}

Visualforce Page

<apex:page controller="wrapperClassController">
    <apex:form >
        <apex:pageBlock >
            <apex:pageBlockButtons >
                <apex:commandButton value="Process Selected" action="{!processSelected}" rerender="table"/>
            </apex:pageBlockButtons>
            <!-- In our table we are displaying the cContact records -->
            <apex:pageBlockTable value="{!contacts}" var="c" id="table">
                <apex:column >
                    <!-- This is our selected Boolean property in our wrapper class -->
                    <apex:inputCheckbox value="{!c.selected}"/>
                </apex:column>
                <!-- This is how we access the contact values within our cContact container/wrapper -->
                <apex:column value="{!c.con.Name}" />
                <apex:column value="{!c.con.Email}" />
                <apex:column value="{!c.con.Phone}" />
            </apex:pageBlockTable>
        </apex:pageBlock>
    </apex:form>
</apex:page>

Now use this code as reference you will get all selected value in your code. You can replace the checkbox with inputradio. and it will solve your problem.