The U.S. Geological Survey (Rantz et al., 1982) have developed nine criteria for an "ideal" gaging site. The criteria are:

straight river part, ground surface conditions and further it depends on the gauging type

No upstream constrictive structures such as railroad trams, road beds, geologic narrows, etc. Gauging station recording should be substantially higher than estimated 1,000-year flood height.

Assuming you do are interested in streamflow, rather than natural channel functions, I would select access and a stable stream section, even bridge site where staff gauge can be installed and peak flow can be measures from bridge.  You want a stable section as much as possible, not actively aggrading or degrading.  I would avoid braided streams and highly sinuous streams sections.  I would probably prefer sections with uniform flow such as a run or glide, rather than a turbulent riffle or slack pool where sediment is apt to accumulate.  

The selection of the watershed to gauge may depend on your intent, goals, project or other determinants, but you should know land use, geology, vegetation, soils, etc. so you are sure you are getting the information desired on flow, floods, etc.  

The transducers that measure gauge height are much less expensive today and easier to install and service, download and process data digitally, as compared to the stream water level recorders with strip charts.  Excessive sediment can cause clogging of transducer (from experience).   

For small drainages or catchments, constructed flumes or weirs can produce high quality results with stream stage when properly installed.  On larger streams or rivers, stream gauging can be a challenge and expensive if you do not have the right equipment and experience (publications available).   Measuring flood velocity across a large floodplain is difficult to do, so in that case, geologic narrows or a well confined channel may be preferred (but Rosgen G and F streams are entrenched, confined, but they can be unstable due to bank erosion and failure, so well forested, brush or vegetated banks with deep rooted plants are often indicators of stability).  If monitoring a wet meadow with sinuous channel, the sedges and rushes have deep and very dense roots so stability should be high, but the difficulty is measuring flows above bankfull during floods.  

The U.S. Geological Survey (Rantz et al., 1982) have developed nine criteria for an "ideal" gaging site. The criteria are:

dear Omar,

The following factors have to be considered in selecting a site for a stream gauging station.

(1) The section should be straight and uniform for a length of about 10 to 20 times the

width of the stream.

(2) The bed and banks of the stream should be firm and stable so as to ensure consistency

of area-discharge relationship, i.e., the cross section should not be subjected to change by silting or scouring, during different stages of flow; a smooth rock, shingle or clay bed is favourable,

while a fine sandy bed is unfavourable.

(3) The bed and banks should be free from vegetal growth, boulders or other obstructions

like bridge piers, etc.

(4) There should be no larger overflow section at flood stage. The best cross section is

one with V-shape, so that there is sufficient depth for immersing the current meter without

being affected by the bed roughness of the stream.

(5) The part of the reach having the most regular transverse section and steady flow

with the current normal to the metering section and velocities in the range of 0.3–1.2 m/sec

should be selected.

(6) To ensure consistency between stage and discharge, there should be a good control

section far downstream of the gauging site. This control may be in the form of steep rapids,

large rocky boulders, restricted passages, crest of weirs or anicuts etc.

(7) The sites above the confluence of rivers are best avoided if the flow is affected by

back water conditions due to the varying discharges in the tributaries.

(8) The stream gauging station should be easily accessible.

best wishes

The river section at the gauging station must be stable, to the extent possible free from eddies, approachable during floods and flood proof, straight river section.

Thank u for all 

There are a lot of good publications on the web. A few examples can be found at the following links:

https://pubs.er.usgs.gov

search for wsp 2175

There are 2 volumes:

Measurement and computation of streamflow: Volume 1, Measurement of stage and discharge

Saul Edward Rantz, and others

1982, Water Supply Paper 2175

Measurement and computation of streamflow: Volume 2, Computation of Discharge

Saul Edward Rantz

1982, Water Supply Paper 2175

NOAA/WMO volumes 1 and 2:

http://www.wmo.int/pages/prog/hwrp/publications/stream_gauging/1044_Vol_I_en.pdf

http://www.wmo.int/pages/prog/hwrp/publications/stream_gauging/1044_Vol_II_en.pdf

British Columbia Hydrometric Standards

http://www2.gov.bc.ca/assets/gov/environment/air-land-water/water/science-data/man_bc_hydrometric_stand_v10.pdf

http://www.geoscientific.com/technical/tech_references_pdf_files/BC%20RISC%20Hydrometric%20Survey%20Manual.pdf

Australia

http://www.bom.gov.au/water/hrs/guidelines.shtml

Hope this helps!

Thank u for all 

The ideal site for stream gauge station is as presented by the U.S. Geological Survey (Rantz et al., 1982).

Thank you very much for all.