SELECT 
  product_id, 
  MIN(price) AS min_price 
FROM 
  cscart_product_prices 
WHERE 
  product_id IN (12, 286) 
GROUP BY 
  product_id 
ORDER BY 
  min_price ASC 
LIMIT 
  1

Query time 0.00043

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost_info": {
      "query_cost": "6.21"
    },
    "ordering_operation": {
      "using_temporary_table": true,
      "using_filesort": true,
      "grouping_operation": {
        "using_filesort": false,
        "table": {
          "table_name": "cscart_product_prices",
          "access_type": "range",
          "possible_keys": [
            "usergroup",
            "product_id",
            "usergroup_id"
          ],
          "key": "usergroup",
          "used_key_parts": [
            "product_id"
          ],
          "key_length": "3",
          "rows_examined_per_scan": 3,
          "rows_produced_per_join": 3,
          "filtered": "100.00",
          "index_condition": "(`atulecarter_new_april_setup`.`cscart_product_prices`.`product_id` in (12,286))",
          "cost_info": {
            "read_cost": "5.61",
            "eval_cost": "0.60",
            "prefix_cost": "6.21",
            "data_read_per_join": "72"
          },
          "used_columns": [
            "product_id",
            "price"
          ]
        }
      }
    }
  }
}