I've been in ecommerce for over a decade and have co-founded and helped start companies collectively driving over $10MM in ecommerce sales. I've consulted for Fortune 500 ecommerce stores. Here's my advice if you're just getting started without a big budget.

Note: Some of this is copied from my answer to a similar question.
#1) PROVE THE ASSUMPTION: Start with a dropshipper's existing products to figure out what sells best before you spend money on manufacturing and warehousing. Amazon is perfect for this - they will pay you 4%-10% to promote 253,000,000 products (http://bit.ly/1q2M85R) - you can sign up at https://affiliate-program.amazon.com/ Alternately, get very small amounts of the product (maybe even just buy some from a competitor) and try selling them on ebay and amazon. Nothing hurts more than having $50,000 of imported product gathering dust in your fulfillment warehouse while listening to a voicemail from a debt collector.
#2) SOURCING
There are several options here. Many people prefer Alibaba.com. Warning - if you use Alibaba, you are stepping into a tank of pirahnas. There are more scam "manufacturers" on Alibaba than real ones. Use Escrow or AliSecure Pay if you buy. If the supplier says they only take T/T, Western Union, Moneygram - just say no! I prefer American Made when possible. If you're like me, try Ariba's Discovery Service - http://bit.ly/1q2NFZu - which will allow you to find suppliers with a physical presence in the USA. Note: Many things can be made on demand (someone purchases, one gets made and shipped) instead of in 500+ manufacturing runs. Start there if you can - Books on CreateSpace.com, Clothes on CafePress.com, Playing Cards on MakePlayingCards.com, etc - to test out your exact product. If you decide to source by purchasing product in bulk, find a fulfillment company to store and fulfill (ship) your orders. Amazon does this - http://services.amazon.com/content/fulfillment-by-amazon.htm - but they might decide to crush you like a bug if you're successful (http://bit.ly/1q2V7DX). Other fulfillment companies for e-commerce include http://www.shipwire.com/ and http://www.webgistix.com/
#3) LAUNCH YOUR SITE
This is an entire topic in itself. One of the fastest ways I know for newbies to start in e-commerce is with a SquareSpace.com store. Other options include GoDaddy.com and BigCommerce.com. If you can stand to use the templates they provide instead of trying to customize them, you'll save yourself a lot of hassle and expense - customization usually looks terrible unless a designer/coder was hired to do the work. If you do customize, find someone on odesk.com or elance.com. If you're not hard up for money, just build a custom store from the start. If you can't do that, save up some money and then go for it. Focus on increasing conversion rate - for every 100 visitors, get 1 to buy. Then 2. Then 4. Then 8 (8%).
#4) MARKET
Figure out where your competition is advertising. Are they getting free, "organic" SEO results on Google? Using social media to drive billions of dollars of sales? (NOTE: That was a joke - don't count on social media as the nucleus of your marketing campaign. Please!) Are they paying for Google ads ("PPC"), buying email lists, using strategic partnerships for promotion, relying on shopping portals, using banner advertising, or something else entirely? There's probably a good reason - figure out what it will take to play in those waters. At the same time, try to find a small enough niche that you can win in it.
#5) BEWARE
Be careful about artsy things. If someone is attracted to something artistic, it's usually because there is a story behind the art for them, or because it's cheap. If you're going to try to sell artistic things, you may want to consider doing some serious research first about who has been successful in that area. Look at etsy.com to see handmade artsy items (very cool).
#6) WORTH A LOOK
Worth checking out as you start your journey: Art.com, yessy.com, Artfire.com, ArtPal.com
#7) DEEP FOUNDATION
If you need help, reach out for a 15 minute call and we'll discuss a go-to-market strategy specific to your goals.