No single, simple answer to that one!

In fact, I'll take this opportunity to put in a shameless plug for the Advanced HPLC Method Development web course that I'll be doing next month (
http://www.lcresources.com/training/tramd.html).
With that out of the way, a few questions:
How much do you know about the compound (hopefully, it's not a case of "Here's a white powder; analyze it.")?
- What's the structure?
Is it ionizable? If so, how many of what functional groups (from which you can make a guess as to pKa values)?
Does it have any double bonds? Any conjugated bond systems or aromatic moieties (from which you can take a guess at UV spectrum)?
How was it synthesized (what were the starting materials and what might be expected in the way of intermediates and byproducts)?
If it's a proprietary compound, do you have any chromatographic conditions from the supplier (or development lab)?
If it's not proprietary, can you find any chromatography conditions for it (or related molecules) on the web?
In the absence of an initial method and assuming no "special problems" (i.e, it's got a chromophore, it's go only a few ionizable groups, and it's got decent solubility in water and/or polar organic solvents), I'd start by making a solution in 50/50 methanol/water and running a UV spectrum.
Then get a good C18 or C8 column. The A solvent would be a buffer at a pH a couple of units away on the unionized side of the pKa (if possible; if not, something like 0.1% formic acid will give you MS compatibility). The B solvent would be either acetonitrile or methanol (flip a coin!). Run a gradient from 5% organic up to 95% organic with the time set to give k* values around 5 (that will depend on the column geometry and flow rate) and see what happens.
If there is only one peak, or if all the peaks are fairly close together (less than about 25% of the gradient), then you can do an isocratic separation. You can estimate the %organic by looking at what the %B was when your compound eluted, and then backing off about 5%. A PDA is very useful here because you can get UV spectra "on the fly".
If you have a lot of peaks spread over more than 25% of the gradient, then you will need a gradient. You can adjust selectivity by tweaking the gradient time, the temperature, the pH, and/or the organic solvent.
If everything comes off at the beginning of the gradient, then try a longer-chain column (if you started with C8) or a different functionality (something like an EPG type column). If everything comes off at the very end, then try a shorter-chain column or something like a cyano.
If your compound has fairly strong acid or base groups (i.e., easily ionizable) and everything comes off at the beginning, then try ion-pair or a mixed-mode column.
Once you get a reasonable separation, go back and develop an "orthogonal" set of conditions: big change in column chemistry, change the organic solvent, possibly change the pH to the other side of the pKa. The idea here is to maximize the chances that coeluting peaks in one system will separate in the other.
LC-MS can be a tremendous help if you have to identify the structures of the impurities. As a minimum (if you don't have access to LC-MS or LC-MS/MS) you should collect enough of your "major" peak to verify that you're looking at the correct compound.
Now comes the fun part

. You need to stress the API and then adjust your separations based on what you see as degradants. Then start all over again with the formulation!
OK, that was very long-winded!

Basically pretty close to your proposal. The major difference is that I really don't find TLC terribly useful as a pilot technique for HPLC; translating from one to the other introduces enough uncertainty that I prefer to work with the HPLC from the beginning. That said, a quick TLC run is a nice reality check in the case of things like crude products or reaction mixtures, where you can see how much junk stays at the origin!).