One thing to keep in mind is that the lowest value amount might not mean that it's also the lowest price if you're working with multiple currency.

Take this example:

Variant priced at USD 1, EUR 1, and GBP 1. Which is the lowest? :)

Here's a quick bit of code that just grabs the lowest price based on the value without taking currency into account:

// Grab any product with variants
Product product = Product.All().First(x => x.ParentProduct == null);

// Find the cheapest price among all prices assigned to indivudla variants and then
// find the variant with the lowest overall price. 
decimal? cheapestVariantPrice = product.Variants.Min(x => x.PriceGroupPrices.Min(y => y.Price));

foreach (var variant in product.Variants)
{
    foreach (var price in variant.PriceGroupPrices)
    {
        Console.WriteLine("Variant {0} priced {1} in {2}".FormatWith(variant.VariantSku, price.Price, price.PriceGroup.Name));
    }

}

Console.WriteLine("Cheapest variant priced {0}".FormatWith(cheapestVariantPrice));