Getting engineers to make plans for projects you'll be doing

Just wanted to ask about this before diving into it, so I know what I’m looking for.

I want to build a wall/fence around my backyard out of concrete blocks, that i’d finish with stucco. I’m thinking maybe 5 feet tall, with thicker concrete columns every 5-10 feet maybe. Sunk foundation of concrete, with steel rebar for support.

Now, I’m not allowed to just start building this, I need to get a permit, and to get the permit, I need to submit the engineering plans for the project. So, I’m about to start trying to find an engineer who will draw my plans for me.

Here’s the questions:
what kind of pay / work would be involved for these kinds of plans (not too specific, I just don’t want to pay 5X what I should’ve because they knew I was 100% clueless).
Do I pay in full once plans are drawn, or after the plans are approved for a building permit?

Any other tips would be greatly appreciated. I really want this wall around my backyard, and prefer it over a wooden fence, so I want these plans. I’m trying to gauge whether or not I should get the plans, apply for the permit, and go from there, or just deal with the fact that wooden fences are easier to put up (from a permitting standpoint)

 I'd like to know where you are located and who told you that you needed these plans. 
 I don't know if this is locally controlled by the city or what, but in my area (Sacramento, CA), it's my understanding that you can build up to 6 feet with block without a permit (3 feet if it's a retaining wall).
 I'll bet that you could download a schematic from a concrete block retailer, and just take those pictures down to city hall with an application for a permit.
 Many home improvement stores have computer assisted drafting programs, and if you bring in graph paper with the dimensions specified, they will print up plans for you.

Wow, that response just made my night. We have no problem doing the install, etc, but hte major hurdle was that to get the permits, we’d need an engineer, which I figured would add hundreds to the process. I’ve posted an ad on craigslist for an engineer to draw these, but no responses to it.

I’ll look into that, my only concern is that the plans would be generic (ie not taking into account the specific lines of my lot, etc) and wouldn’t pass. I dunno, I’ll def look into that, because we were goign to waste hundreds to put up a crappy fence (for backyard privacy), until we could get the plans/permits/etc for the masonry fence.