I would like to try to express the things simply and efficiently:
1.) "I would like to set up a website selling childrens clothes etc online."
You need a online shopping cart or web store. It is a script/package, You can install it in your web server. If you install it:-
-> you can add/post your item's titles, photos, categories, descriptions, prices, shipping methods, etc.
It is free of cost (because most of them are avail for free / open source projects)
-> And you need to integrate a payment method (e.g: paypal, 2co, google chechkout) to receive payments from your buyer. Most of such services are free to join and integrate. They only charge a small % fee from your sale. (Because, they give you a secure interface to receive payments from your buyer, and pays you without any head-achs).
2.) "I have purchased the domain name from namesco" & "what is hosting? is it compulsary?"
If you already buy a domain, you can use it to host your website (without transfer charges. see below step 4).
"Domain" means "an address/name" and "Hosting" means "a (built house or) store".
If you use your address without a house/store, your visitors will go to another store/shop to shop/buy something.
or, If you have a store without an address, no one can't find/reach it.
So, a domain (address) and hosting (store) are two sides of a coin/website.
If you have both of them (a well built store and an address/name), your visitors can find you, view your items and can buy them.
Domain registration (only costs about $6.10 annually!) is cheaper than buying a domain.
Sure you must choose a domain registrar who give you full control on your domain. (some companies keep your domain's most of controls at their side to charge you often).
Hosting will costs less than $100.00 annually.
While choose a host, you must look at their support. It is very important. Some companies does not support everything, some others not support on your website related matters (e.g: installing a package for you, shopping cart or web store related settings, file editing, ...). And some others do anything for you, but charge you often.
3.) "So.. my next move is to look at desinging the website"
If you install a shopping cart package, you can apply free themes on it. So no need to spend extra for designing. most of themes are free of charge, a lots of free themes avail online. (your company may be try to sell it. You can go with free one!)
If you want to design your website, it will be takes a long time. And you will have to pay a sum (for your electricity, books, Internet Fees, Energy, Time, Days, Months, etc.).
And you need to have a good experience to create a webstie which works well on most web browsers (Firefox, Internet Explorer, Opera, Netscape, Chrome, ...), various operating systems (windows 7, 8, 95, 98, ME, XP, 2000, Mac OS 6, 7, 8, 10, RedHat, Ubuntu, KDE, ...). Because in Internet, one visitor may come to your website from his P2 + 128MB RAM + Netscape browser + Win95 or Linux, and at the same time, another one may come with her i7 + 8GB RAM + Opera Next + Windows 8!. But your website should works well in all time, all machines (PCs).
So best is, paying a good developer (not designer. Designer is may not well in creating a shopping website. Because, shopping websites are dynamic, database driven applications.) Programming (coding) will build such a website. This is only you really want to develop your website without any free shopping cart/store packages. (In other word, if you use free packages, you can save these costs.)
4.) About transfer:
No need to transfer/change IPS to host a website. Just point your domain to your host. If you have a domain, log into its management account or control panel > find host or point or DNS settings > give it to your hosting company's DNS.
If your domain manager does not allow you to change DNS, contact them to do so.
If they refused, then it is best to get back your domain such a domain manager. So, start transfer. But it will be about $6.10!
If you have not had a domain yet, register a new one with your hosting company. It is easy to manage.
5.) I hope all of above will clear your doubts and helps to proceed next. I'm experienced (over 10 years) in web technologies, administration, development and server management. If you want any help/assistant, don't hesitate to contact me: mnr@1webcare.com (No need to be our customer or client. I'm open minded, I just try to help you with my knowledge (personally). Thats all. You can buy your domain/hosting anywhere.).
Have a great day!