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Hello. 
The bathroom was designed keeping in mind every request you had. I have copied here links of every furniture and item used in the model, to buy directly online and price calculations. All items are from IKEA /Home depot/ Lowes stores. The budget goes to 1570$, since you mentioned you can tolerate up to 20000$. 

List and links of the furniture used:
 
-Double sink cabinet: 
http://www.ikea.com/us/en/catalog/products/S19023450/
 
-Faucets :
http://www.ikea.com/us/en/catalog/products/20281297/
 
-Mirrors (with LED lighting integrated):
http://www.ikea.com/us/en/catalog/products/10250084/
 
-Ceiling Lighting:
 http://www.ikea.com/us/en/catalog/products/70082511/
Bulb for the lamp:
http://www.ikea.com/us/en/catalog/products/20266225/
 
-Toilet paper holder:
 http://www.lowes.com/pd_367180-69133-4713_4294639617__?productId=3606194&Ns=p_product_qty_sales_dollar|1&pl=1¤tURL=%3FNs%3Dp_product_qty_sales_dollar%7C1&facetInfo=
 
-Shower faucet:
http://www.lowes.com/pd_89235-72981-T14286-SHQ_4294737295__?productId=3139897&Ns=p_product_qty_sales_dollar|1&pl=1¤tURL=%3FNs%3Dp_product_qty_sales_dollar%7C1&facetInfo=
                Tub/Shower Rough-in:
http://www.lowes.com/ProductDisplay?partNumber=250516-72981-R10000-UNBX&langId=-1&storeId=10151&productId=3284788&catalogId=10051&cmRelshp=req&rel=nofollow&cId=PDIO1
 
-Towel Rail:
http://www.ikea.com/us/en/catalog/products/90162597/
 
-Tower Hook:
http://www.ikea.com/us/en/catalog/products/40149396/
 
-Wall paint color:
http://www.homedepot.com/p/BEHR-Premium-Plus-1-gal-Ultra-Pure-White-Semi-Gloss-Zero-VOC-Interior-Paint-305001/202761530?N=5yc1vZbbbgZ1z140hb
 
-Shower tiles:
http://www.homedepot.com/p/Daltile-Matte-Artisan-Brown-4-1-4-in-x-4-1-4-in-Ceramic-Wall-Tile-12-5-sq-ft-case-0744441P1/202627046?N=5yc1vZarszZ1z0tni8#product_description
 
-Floor tiles:
http://www.homedepot.com/p/qv/202646464


Prices and budget calculation:
-Double sink cabinet:                                                               $     649 
-Faucets:                      $   70 x 2                                            $     140
-Mirrors:                      $ 129 x 2                                             $     258
-Ceiling lamp + bulb:                                                               $      15
-Toilet paper holder:                                                                $      19
-Shower faucet + Rough-in:                                                      $      233
-Towel Rail + Hook:                                                                $        30
-Wall paint color:                                                                    $        30
-Shower tiles: 32.5$ / 12.5sq ft.   32.5 x 5                                  $      162.5
-Floor tiles:     17.3$ / 11 sq ft.      17.3 x 3                                $        52
                                                                                                __________

Total:                                                                                                        $    1570