For planning interior walls, should I get an architect or interior designer or someone else?
I would not let a designer make these kind of decisions.  A good architect, a builder, or a good general contractor would be your best bet.  You could always bring in a city inspector and ask them for a few thoughts too.  

If money is no object than almost anything goes with a basement.  You can basically put a wall anywhere as long as you aren't moving anything above your head.  

Some of the things to think about when drawing up plans:


How do the stairs flow?  I really do not like basements that have stairs that slice the basement in half (unless you have a huge basement).  I also do not like stairs that have a minimal landing pad - meaning it is hard to get things in and out of a basement.  The stairs in your situation could be good to go and a non-issue but this is the first thing I think about with a basement remodel.
Where are the low points of the basement ceiling and how will we handle these.  In a normal basement you will have a main load bearing beam that runs length of the house.  How high is it?  I am also assuming you will have duct work running parallel to this beam.  Can we go 3 inches under the duct work and beam and still have good clearance (7 feet).  Basements with lower clearances, I like to put the duct work against the edge of a room, with a higher clearance it doesn't matter as much.  Also the last few I have done, I have not enclosed the beams/duct work, and instead painted it with autobody paint.  Saves room and gives architectural details.
Where is the main stack and plumbing located?  If the mainstack is in the middle of the house - which is pretty common - then you not only have an obstacle but you have a huge cost if you want your bathroom in a far corner.  For instance by creating your bathroom next to the stack and incoming water supplies you could save 5-10K.  Plus bathroom could hide stack - I have built larger closets to do this next to or in bathrooms.  And then to add on a lot of people just put a bathroom in a plan and next thing you know you can take a crap and watch the football game without leaving the toilet.  Give your bathroom privacy - put the entrance in a hallway.
Windows...  Are they currently suitable for what you want?  If you have bedrooms downstairs do you need bigger windows to meet code?  What is the cost of this?  Also when building rooms you want to leave at least a half foot from edge of window to wall.  
HVAC and drain.  Hopefully these are in the same area.  Also there are building code requirements for room size.  This is why it is usually a good idea for this room to be a storage room also.  And with the drain, obviously your basement is pitched (at least in some areas) to drain water to it.  So you can't build a wall a foot from it and not expect issues (drain back ups should not spill into walls).  
Electrical panel.  Your panel needs to be accessible and have clearance.  Do you want the panel on a wall in a living room?  Best bet is to make this part of storage/HVAC room but that always doesn't work out.  You can move panel to fit plans (lots of money) or you can design around it.
Learn about existing walls.  If you have no walls in your basement that is a plus.  Often though basements are built with a divider wall or the storage room walls up.  You must figure out what is inside these walls and if you can use these walls in your design.  I had a divider wall in my basement that I used.  It was at a good spot but wish I would have know it was at about 85 degrees from floor.
Getting your money back.  You are building on a walk up basement.  It is an investment.  If done right and you do some of the work yourself you could see a return on your money.  Basically to make money back you need three things.  Bedrooms, full bath, and functional space.  Bedrooms are first priority - so make sure they meet "bedroom code" - windows and closets.  Closets are sneaky.  Plan for them if  you want something to be a bedroom.  Full bath is worth it.  You don't have to create a spa but if you have a bedroom get a bath in.  If your house won't meet code for bedrooms then a half-bath or no bath is fine - but then I would keep the basement very open so it could have multiple uses.


There are probably lots of other things to think about but this is just off the top of my head.  When designing you need to figure out your storage/HVAC room and bathroom and then kind of work around those two things.  Something that is properly designed can easily save 10-20K in a basement remodel.

Note: I was hesitant to mention getting an architect involved.  I lump architects into two general groups for residential housing - functional/builder and the fancy/designer.  The functional/builder will work with what they are given and cost structure.  They will understand how to integrate electrical panel and storage room.  Might even have some good ideas on room transitions and such.  Going with the fancy/designer architect doesn't mean they don't know what they are doing, it is just the design and look come before cost.