I have developed a product that I would like to get to market through
distribution channels. In the "lawn and garden" industry what would be
a typical rate that I would be charged by a distributor for moving my
product? If this is based on price, I have two scenarios: a wholesale
price of $28.00 with a suggested retail price of $49.00 and, a
wholesale price of $37.00 with a suggested retail price of $64.00.
Also, would I pay the freight cost to deliver the product to the
distributor?

You need to start at the retail price and work backwards.
If the product retails at $49, then subtract the retail margin. This
would be between 20% for a large discount store to 33.3% for a smaller
neighbourhood outlet. Let's take 30% as an average, so the retailer
will pay $49 less 30% = $34.30.
Generally, he will buy it from a distributor who will want around 25%
margin for the storage, sales, secondary distribution (from warehouse
to retail store). So the distributor will pay $34.30, less 25% =
$25.74 for the product, delivered to his warehouses in each region.
The manufacturer will generally have to pay "primary" distribution to
the distributor's warehouse, but this can often be included in the
distributor's fee as an add-on service. The exact cost depends on the
value/mass ratio of the product. ie Lawn dressing will cost a very
high % to distribute, whereas a computerised controller for a watering
system will not. As a rough guideline, products like groceries average
out at about 6% to distribute, so let's say 10% for a garden product.
The manufacturer then gets $25.74 less 10% for the product = $23.15.

This is around 47% of the retail price. In my experience of food
marketing, primarily through large food stores, I used to work on us
getting only 40% of the retail price, after paying all the additional
expenses that stores like to add on.