C# MVC checkbox javascript ajax or C# action which way should I do?

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C#

Javascript

Ajax

MVC5

Hello everyone,
I have a view that has a table with rows of records. In front of each row I added a separate checkbox. I am currently in the process of determinine if this checkbox ischecked or not. I was wondering if I should do my button click with javascript and ajax to determine what records have a selected checkbox with these checkboxes I will print out a rdlc report of what was selected. Or should I use a HTMLActionlink button to go straight to a controller and see what was selected. What way would be faster and better? Also what is the proper way I should do this?

MVC View
<input type="button" class="btn btn-primary" name="command" id="btnGetChecks" value="Generate Selected" />
<table class="table" id="maintbl"><thead>…</thead>
<tbody id="maintblbody">
                @for (int i = 0; i < Model.ListQuotes.Count; i++)
                {
                    var current = Model.ListQuotes[i];
                    <tr>
                        <td>
                            @Html.CheckBox(i+"_Row", true, new { value = @Model.ListQuotes[i].QuoteID })
                            </td><td>
                            //<input type="checkbox" class="checkbox" name="checks" id="@(i + "_Row")" value="@Model.ListQuotes[i].QuoteID" />
                        </td>
                        @for (int j = 0; j < Model.Settings.Columns.Length; j++)
                        {
                            if (Model.Settings.Show[j])
                            {
                                var quote = current.GetType().GetProperties().Where(x => x.Name.Equals(Model.Settings.Columns[j])).First();
                                <td style="padding-right:20px;">@quote.GetValue(current, null)</td>
                            }
                        }
                        <td>
                            <button type="button" class="openModal btn btn-danger" data-quoteid="@Model.ListQuotes[i].QuoteID">
                                Edit
                            </button>
                        </td>
                    </tr>
                }
</tbody>
<script>
$('#btnGetChecks').on('click', function () {
            var quotes = [];
            var quoteid = $(this).attr("value");
            var chkboxtable = $('#maintbl');
            var 
            //$('input:checked').each(function() {
            //    quotes.push($(this).attr("value"));
            //});    with 0 -  ^(0|\+?[1-9]\d*)$         /^-?[0-9]+$/
            // $(this).val($(this).val().replace(/[^\d].+/, ""));
            // if (!(keyCode >= 48 && keyCode <= 57)
            $('input[type=checkbox]').each(function () {
                if (this.checked==true) {
                    if (IsPositiveInteger(quoteid)) {
                        quotes.push($(this).attr("value"));

                    }
                }
            });

            alert(quotes);
        });
<script>

What I have tried:

Here is what I currently have im very curious to hear what you all have to say. I have the id of each quote attached to the checkbox. I wanted to push the valid ones to an array but so far my current code doesn’t do it yet. I feel I am close to having it.