Here's the deal. As a SP, you are the business and the business is you. Therefore if someone sues the business, they are suing you, and all of your assets, except those specifically protected by law, can be seized if you were to lose a case. Additionally, you could have long term restitution forced on you as an individual, even if you were to close the business.
Nevertheless, quite a lot of people set up business as a SP because it is easy, it is cheap, and finally, taxes and annual reports are simpler than reporting for other business vehicles. So, if you are a garung guni, life is simple, the chances of you being sued are about nil, and a SP works just fine. If you are undertaking a business that involves business risk to others, for example, investing money in your business in exchange for future profits, then you may not want a SP as the dissatisfied investor might want to sue you for failure to meet your promises.
If you do go the SP route, you will most certainly want to keep separate bank accounts and financials for your business, as many people have run afoul of tax laws by mixing personal and business together. Additionally, it can be more difficult to get business credit cards, loans, or lines of credit from banks when you are a SP. In short, if what you are thinking about is small potatoes and relatively risk free, then a SP is OK.
Technically, there is no such thing as a LLC in Singapore. For example a LLC (limited liability company) in the USA allows me to be a sole proprietor and file my taxes that way while still having all the protections of a corporation. I am not a shareholder in my company, nor am I a director, I am a member of the LLC.
In Singapore, you would form an exempt private limited corporation. You would be the sole shareholder (with as little as one dollar in shares), and you would be the managing director with responsibility for running the company.
You are indeed protected from lawsuits (most of the time - see below), and the most you can lose is everything in your company and the total amount you invested. Your personal assets are not generally at risk.
There are a couple of exceptions to the above. First, as a brand new company, virtually anyone or any company that is going to extend you credit will also want you to take personal responsibility for any debts that arise by signing as an individual. This pierces the veil of corporate protection because you have personally signed.
The other exception is that you can be sued personally as the director if your company is guilty of some kind of corporate malfeasance. For example, let's say you offer stock to investors, then commit a fraud or steal the money. You would be personally liable as a director for actions within the company. Note that if you are simply stupid, make bad decisions and bad investments so that the investors lose all their money, you are protected by the corporate shield... you may be stupid but you are not criminal.
Banks and suppliers tend to look more favorably on private limited businesses than a SP. You tend to have more "gravitas". Someone who goes to all of the trouble to form a pte ltd just looks like they are more serious about running a business.
The downside to a pte ltd is the reporting complexity. As a single director, you must have an outside secretary... could be mom or dad... but a person who knows what you must do to properly run a pte ltd. For example, with a SP, you just run on down to the bank, show them your registration from the ACRA, and you are good to go. With a pte ltd you must bring a signed director's resolution to the bank, and enter it into the company minutes book, in order to comply with the Companies Act.
Tax filing is more complicated. You have to make yearly reports to ACRA of directors, shareholders, stock held, secretary name. You need a registered office, which can be your home. It costs more on a yearly basis, just to keep a pte ltd alive. On the other hand, if you're serious about starting a real business and you will be subject to real business risk, then the pte ltd is really the way to go.
I'm no expert in HDB, but here is your primary consideration. If you are using your home to run your business, and it generates little or no traffic or congestion at your flat, then you are good to go. For example, you could be an accountant who does most of his work online, with his clients stopping by just every once in a while to sign documents. That would work.
But, if you decided you were going to be a small appliance repairman, and you had a steady stream of people dropping off and picking up appliances, then you'd be running a business out of your house and that wouldn't work.
So... you say you're going to start a drop ship business from your house. Where do you plan on keeping your inventory? Where will the repackaging and shipping be done? See, if you had UPS or DHL come with a package every couple of days, and once a day you take a bunch of stuff down to Singpost, you'd probably be OK. But, if you had helpers or a steady stream of traffic, you would soon have troubles to deal with. Of course, if the actual dropship activities are happening elsewhere and you are simply running it from your house, all is good.