Welcome Antony,
If you are not a designer yourself, we have seen lots of sellers just go to Upwork or FIVERR to find a designer who has experience with Shopify brand and theme design. Usually they can do it less than 8 hours. Of course you can always just purchase an existing Shopify theme that you like. There are also lots of Shopify theme/design app that you can take a look as well (i.e. Gempages). It depends on your budget and how much efforts you want to put into your brand.
For fashion dropshiping suppliers, getting 1 - 2 days shipping will be really challenging unless you buy wholesale and stock up yourself using 3PL. We have seen successfully sellers use Trendsi dropshipping to test out different products by buying samples and promoting on social media, and as soon as they identify the best sellers, they will buy wholesale to lower cost and store at Trendsi warehosue (we also provide 3PL service) so that it can be shipped faster with more stable inventory.