Take a look at the relevant bits of the database description for that table.
Field Type option_name varchar(64) option_value longtext
The key is 64 characters max. The value is longtext which should be more than you need.
To have you caching work, you need a unique value for the key, but it doesn’t have to be readable. My suggestion would be to hash the GET string. It should be unique and well shy of 64 characters.
Instead of this: $name= base64_encode(serialize($_GET));
Try this: $name= wp_hash($_GET);
Proof of concept using the sample GET string above:
$str="?search_type=product&relation=or&date=all&s=tagsearch&merchcat=cotton&brand=brandx&color=blue&etc=morestuff";
var_dump(base64_encode(serialize($str)));
// vs
var_dump(wp_hash($str));
Edit based on the discussion below (thanks @G-M):
The order of the arguments in the GET string could effect the hash values. The safe thing to do is to normalize the array. The following should do that:
$str = $_GET;
ksort($str);
$str = add_query_arg($str,'');
$str = wp_hash($str);
var_dump($str);
All arguments are preserved, even the empty ones, which seem to be what the OP wants, though I personally believe that running the array through array_filter to remove empty values would actually provide better caching.
$str = $_GET;
$str = array_filter($str);
ksort($str);
$str = add_query_arg($str,'');
var_dump(wp_hash($str));
No data validation/sanitization was attempted.
When you save that key to the database, I would also suggest prepending a string to make it identifiable– something like $str="my_plugin_slug".$str before saving it.