Personally, I'd be more worried about a client base. The rest is easy. I don't know much about the chemistry end of the patent practice and what clients are like, but I imagine your clients will tend to be larger companies rather than individuals. As a person in solo practice trying to find interesting ways of marketing my practice, I'd be interested to here how you approach this if getting clients isn't a problem for you.
Now, on to your questions.
Docket numbers. How do you intend to identify your cases within your practice? As far as I know, every attorney as a system of identifiers which are sorted in some manner such that the attorney can find the case file in the filing cabinets. I don't see how you can do that without some sort of ordered system of identifiers. So, while docket numbers aren't required, it's a practical necessity to running any practice I'm familiar with.
As for your proposed numbering system, it's fine as far as I can tell. I chose a straight sequential system. Files for a single client are not contiguous. The reason for this is that it's possible that a new matter for an early client can over-fill a file drawer early in the sequence of files, requiring re-distribution of files within drawers relatively frequently and at times not selected by me. In my system, the only major file shuffling happens to re-pack periodically to reclaim space left by closed/archived files. And I can choose when that happens. This kind of dense-list vs. sparse-list processing is second-nature for CS majors.
Deposit Account in the USPTO:
I don't have one. I write checks, and have since I started my solo practice in 1995. At the time, I was filing cases in batches for large entities. One night, I filed 10 cases, each with filing fees in the range of $1,000-2,000. That means I would have to have had $20,000 in the account. If any other matters come up, the account would be severely depleted. I guess I just didn't want to manage yet another account. And, it always bugged me that I would have $10,000 or so (the amount I thought I could get by with most of the time) just sitting there. And, that particular client with the $20,000 night takes a good couple months to pay the invoice, so that's quite a hefty float for a small-timer.
I suppose now I should probably start one to cover incorrect amounts in the amount I pay. But it's never been a problem. I can't think of any situation in which you aren't given an opportunity to correct an incorrect fee payment. Maybe one exists, but I just can't think of one right now.
HOT TIP FOR PRACTITIONERS: Here's what I recommend. Get a frequent flyer miles credit card for your practice (if you don't already have one). Keep some headroom on it. Use it for fees (form PTO-2038). Bill the client immediately. The PTO generally takes weeks to months to get around to taking the money from the credit card (or bank if you use checks). When the client pays, pay the credit card off and you should never pay any interest (or at least not much). And, you should rack up the flyer miles like crazy.
If you don't have the need or want to fly, pick a credit card with another perk.
<cont.>