To be honest there almost no different between any domain registrar/reseller offer. Generally all are good. You can get domain name and hosting from Exabytes to make it easier. However when it comes to full website development there basic rule of thumb that you shouldn't put all eggs(domain name & webhosting) in one basket.

It is advisable to buy from domain provider who sell domain as their main product(eg : NameCheap/Name.com) and get webhosting somewhere else(eg : Exabytes). This is not necessary but it does eliminate future complication if you want to change webhosting. If you're new to domain name and webhosting, I would suggest you to get both from the same provider.

Any usual Linux webhosting provider should have no problem with OpenCart, Prestashop or any other php e-commerce platform. Being e-commerce platform, all have built-in shopping cart. You just need to add payment processor/gateway to receive payment from customer

Do some reading on payment gateway of the platform you choose, commonly payment processor like Paypal/Payza is the easiest and you don't need to pay anything to use it but if you want to be able to receive local bank transfer from your customer you need payment gateway like ipay/molpay etc

But are you sure you want to handle the setup and the business/management side yourself? E-commerce platform is a b*tch(to setup and maintain) and I would highly recommend using hosted solution like Shopify or Prestabox for people who just want to sell their product.

Any particular budget?
Just an advice, make sure you ask your prospective host first whether e-commerce platform that you choose will work well with their particular plan. I've heard that Magento are slow/unresponsive on shared hosting