This is essentially what I do. I tried washing yeast and had mixed results and figured that starting with clean yeast might be a better way to go. I've only been brewing a couple of months, so I can't yet personally vouch for shelf life, but others here have stated that reusing harvested yeast 6 months to a year later is not uncommon.
When I get a new pack/vial of yeast, I make a starter with 120g DME and about 1200ml water. Add the yeast and let them do their thing on the stir plate for about 48 hours. In the meantime, I boil two 8 oz mason jars & lids, fill them with boiled water, and let them cool to room temp. After the starter is finished, I empty the mason jars, swirl the flask so that the yeast is in suspension and fill up both jars, then secure the lids and refrigerate. I also put the flask in the fridge until brew day. When it's time to brew, just decant and pitch. Since I usually do 4g batches, the remaining yeast in the flask is usually enough according to
YeastCalc, but if it's not, then I'll do another step up to get the count up to where it should be.
When it 's time to re-use saved yeast, I do a two-step starter (50g DME/1000ml water & 120g DME/1200ml water) over the course of a week or so. By using the above DME/water ratios, the first step is at ~1.02 OG and the 2nd ~1.04. The reason for this is that I figure the viability of the stored yeast may be somewhat compromised, so I'm trying to ease the yeast back to life with the lower OG wort first, then let them go to town with the normal OG wort for the 2nd step. When the 2nd step is done, I'll save off one mason jar as explained above and pitch the rest once it's been chilled and decanted. This way I always have 2 jars in my yeast bank and I always use the older one first.
This system has been worked pretty well for me so far.