First - an apology for the length of the following.  I rarely write long posts, but this one, I am sure, delves deep into TMI (too much information) territory.

My very best advice would be to contact a respected, time-proven sound consultant who has a successful past experience in designing theatrical sound systems.  This consultant would meet with you, determine your needs, design a system around those needs and then bid the job out to sound contractors who have a proven track record with installs in spaces such as yours.

If you don't think you can swing the extra expense of working through a sound consultant, then your next best bet would be to contact several sound companies who have a proven track record of successful theatrical installs and allow them to evaluate your space and create a system design and proposal for you to review.  You would then choose what you determine to be the best design.

A few, more specific, suggestions:

If the current sound booth is not on the main audience floor and open to the room (allowing the sound operator to hear the exact same sound mix that the audience hears), then that would be priority one.  Even if you have to sacrifice a number of seats - get it on the floor!  This is one of the most critical improvements to theater audio that can be made.

The proper design and installation of the main speaker system is another crucial consideration that will either allow the audio portion of your productions to succeed mightily or fail miserably.  The difference in "just hanging three speakers where they look about right" and a professionally designed, installed and tuned FOH speaker system is marked.  Even if you have access to technicians who are experienced and capable of doing minor install work, I would again advise that you at the very least have the main ("FOH", "house" by other names) speaker system professionally designed, installed and tuned.  If you truly want to make the new system  "very impressive for ... patrons" this is where to start.  If budget allows, the inclusion of a subwoofer (low bass producing) speaker system would be a significant step toward the desired "wow" factor.  Not only will it fill out and support any and all musical material played through the system - a subwoofer system is indispensable in providing high-impact low frequency sound effects, such as thunder, earthquake, explosions, etc.  Regardless of initial budget allowances - a good subwoofer system should be a part of every theatrical system and it is an upgrade which you could make later. 

The layout of audio components in the audio booth should place all controls which are regularly adjusted during a production within easy reach of the operator(s).  If budget allows, a digital mixer with scene memory would be a great way to go (Yamaha LS-9 and similar) - allowing you to program and call up scenes/groups of actors as the production progresses.  These mixers also possess quite impressive signal processing (equalizers, compressor/limiters, reverb/digital effects) which can eliminate the need for some of these items in the form of stand-alone rack mountable gear.  If budget will not allow the purchase of a digital console, there are many quality analog mixers on the market with more rudimentary input grouping capabilities that will serve well.  Just leave yourself some room to grow when choosing a mixer (when 33 channels become necessary - 32 just won't do...).

Whether the components are provided in analog or digital form, the following is a (very loose) list of basic ("essential" as you mentioned) needed components:

Microphones: Wireless/wired area/wired boundary/hand-held vocal mics (wired or wireless)/piano(?)/ as needed

Mic Cables: for area, boundary and wired hand-held mics

DI boxes for plugging instrument-level sources (guitar, keyboard, etc) into the onstage mic inputs

Cables for DI boxes

Floor boxes/stage boxes for microphone input (preferably spread throughout the stage area for easy access)

Effects playback capability: from computer effects databases piped in via USB, CD effects libraries, devices such as 360 Systems Instant Replay, etc.

CD Player(s)

Mixer (with as much built in flexibility as you can afford)

Effects processor(s): for vocal and instrumental effects (and anything else you might to process through them.

Signal processing equipment for the main speaker system (equalizers, compressor/limiters, delays for signal alignment, cross-over networks to divide frequencies between speakers and speaker components.  * these can all be individual rack mount type processors or may be combined in certain fashions in "all-in-one" type digital signal processors.

Amplification for main speaker system

Signal processing and amplification for each onstage monitor system you wish to provide.

Speakers for main house and monitor systems.  -  Appropriate makes and models of main loudspeakers will be determined by the shape/seating arrangement/acoustical properties of the room itself.  Low profile monitors are more aesthetically pleasing in a theater setting.  Yamaha has recently release and excellent "install series" floor monitor which incorporates a 90x60 degree rotatable horn between two 8" woofers.  It is very low profile and sounds superb with very little EQ.

Effects speakers which are movable and can be hung anywhere in the auditorium where a special, localizable (is that a word) effect is needed - this is something that could be added later if budget dictates

Line-level and speaker-level cabling for all of the above.

Intercom system and wiring from party-line systems to elaborate multi-channel systems

Racks for all of the outboard amplification, signal processing and playback equipment.

Power sequencing system with booth-located on/off switch - this is a system which automatically powers up and powers down the system in stages and in the proper order to avoid overtaxing the electrical system as well as eliminating possible damage from neglecting to bring the system up or take it down in the proper order.  A Furman ASD-120 or similar such sequencer works very well and is dead reliable.

AC for all of the above - with the sound system on its own dedicated technical power supply.

AC and audio Installation labor, conduit, rigging hardware, etc for the above.

Overall system cost?  This is a grossly loaded question and the expenditure possibilities are all over the map.  The components mentioned above are intended to be good, solid quality components from respected, well recognized companies.  None of the gear needs to be "esoteric" or "exotic" to perform well.  For a 250 seat theater?  A professionally installed system could run anywhere from maybe the $75,000 - $100,000 range to "the sky's the limit".  Some money can be saved through the use of your own skilled house technicians (if such exists).  Some install companies may agree to utilize some of your "qualified" personnel to provide some of the install labor (but this is rare and usually they would rather not for quality control/liability/etc. reasons). Having the typical local music store design and install is typically (note I said typically) a bad idea and most often (most often - not always) results in substandard design, installation and support.  There are rare exceptions.

Some final notes (as if everything has already been covered - it hasn't):

Any and all respectable installers should be expected to provide you with a complete as-built system diagram, rack drawings, all equipment manuals, written system warranties, and such.  This should be standard operating procedure.

It is perfectly OK (and advantageous) to express contractually any expectation you might have: start date, finish date, payment concerns, general quality level of equipment expected, general quality of installation, documentation – anything that is important to you – anything that might keep you up at night worrying because you didn’t put it in writing and didn’t have signed by the contractor.  It’s your system and you will be using it for years to come.  It has to do what You need it to do. 

Insist that the electrical provider respect the needs of the sound installer.  AC circuits can have a profound effect on the overall operation of the system especially with respect to achieving clean sounding hum-free/buzz-free audio. 

Good luck on your new system project.

Regards,