Following is the list (regularly updated) of top-rated apps that are "ACTUALLY USEFUL" for most users and also aren't very resource hungry (Apps are recommended for devices with Android 4.0+).
  1. Launcher - Nova Launcher, (Prime)
  2. Browser - Naked Browser Pro, Opera Mobile (with Off-Road mode)
  3. Keyboard - SwiftKeyFlesky (No Swype)
  4. Alarm Clock - Alarmy (Sleep If U Can), Sleep Cycle alarm clock
  5. All-In-One (Multi-purpose) Apps - Smart Kit, All-In-One Toolbox

    COMMUNICATION -
  6. E-Mail - K-9 MailMail.ru
  7. SMS ZERO SMSTextra, GO SMS Pro
  8. Instant Messaging - WhatsApp, Signal Private Messenger, BBM
  9. Video Calling - WhatsApp, JusTalkSkype

    SOCIAL MEDIA -
  10. Facebook - Facebook Lite, Metal, Friendly or Mobile Website (with notifications turned on) 
  11. Reddit - Reddit, reddit is fun, Relay for reddit (Pro), Sync for reddit (Pro)
  12. Forums - Tapatalk
    PHOTO & VIDEO CAPTURE -
  13. Camera - Open CameraCameringo+, Z Camera, Facetune
  14. Drawing - Adobe Capture CC
  15. Screen Recording - Screen Recorder, DU Recorder
  16. "Secret" Video Recorders - SVRSecret Video Recorder

    PHOTO & VIDEO EDITING -
  17. Image Editor - Pixlr,  PhotoDirector, PicsArt Photo Studio
  18. Photo Effects & Filters - PicSay ProSuperPhoto
  19. Stop motion Videography - PicPac
  20. Video Editors - VidTrim Pro  

    MUSIC PLAYBACK -
  21. Audiophile Music Player - Neutron Music Player
  22. Simple Music Player -  Pretty Good Music Player, Pi Music Player
  23. Stream Music (while screen is off) - SpotifyYouTube Music

    VIDEO PLAYBACK -
  24. Video Player - VLC321 Media PlayerVideo Player Perfect
  25. Youtube Video Player (Also can stream Music while screen is on) - Og YoutubeNewpipe

    AUDIO APPS -
  26. Emergency Alerts Radio - Scanner Radio Pro
  27. Melodies/Sounds - Relax Melodies
  28. Audio Enhancers - FauxSound Sound Control, ViPER4Android
  29. Music Recognition - SoundHoundTrackID™

    WORK BASED -
  30. Document-based Work - WPS OfficeOfficeSuite, Polaris Office
  31. PDF Annotation & Markup - SquidezPDF
  32. Document Scanner - Office LensTurboScan, CamScanner, Business Card Reader Pro
  33. Book Readers - Moon+ Reader Pro, Aldiko Book Reader
  34. Jobs - Resume Builder Pro

    NOTE TAKING -
  35. Lectures - LectureNotes, LectureRecordingsSquid
  36. Calender + Notes - Calengoo aCalendar+, ColorNote
  37. Save Notes For Reading Later - Pocket, Clipper Plus (with Sync)

    INTERACTION ADDONS -
  38. Notifications - Notific Pro, Touchless Notifications Pro
  39. Widgets - Beautiful Widgets Pro, Elixir 2 - Widgets, Multicon Widget

    INTERFACE MODS -
  40. Theming Engine - SubtratumArcus
  41. Interface Addons - Status Bar Mini PRO
  42. Display Mods for Sleeping - TwilightLux Auto Brightness
  43. LED Control - Light Flow Pro - LED Control, Light Manager - LED Settings

    WEATHER -
  44. Weather - Weather & Radar, 1Weather, Amber Weather
  45. Weather Reports (Detailed) - Weatherbomb
  46. Weather Daydream - YoWindow

    FILE MANAGEMENT/EXCHANGE -
  47. File Manager - Root ExplorerX-plore FIle ManagerES File Explorer/Manager PRO
  48. Cloud Storage - Autosync Google DriveGoogle DriveDropbox 
  49. Data Sharing -  Xender, SHAREit

    PHOTO & VIDEO MANAGEMENT -
  50. Gallery - QuickPic
  51. Photo Organizer - Slidebox
  52. Pinterest - Pinhog

    REMOTE PHONE MANAGEMENT -
  53. Manage Phone through PC -  AirDroid
  54. Streaming (for DLNA/Chromecast, etc) - BubbleUPnP
  55. Remote PC Control - TeamViewer, Unified RemoteSplashtop Remote Desktop

    GAMING -
  56. Gaming - FPse, Sixaxis Controller
  57. Game Development - Coda Game
  58. Game Performance Enhancement - GameBooster 3CM Gamebooster

    SENSOR BASED -
  59. Product Scanner - Google Goggles
  60. Maps - OsmAnd+Google Maps, MAPS.MEMapFactor, GPS Navigation & Maps Sygic.
  61. Sensors for Data Measurement - AndroSensor, SatStatSensorium, Ulysse Speedometer Pro, Runtastic Heart Rate PROGPS DataGPS Data and Toolbox
  62. Cars - Torque Pro (OBD 2 & Car)

    NETWORK -
  63. Network Management - Fing
  64. Firewall - AFWall+, NoRoot Firewall 
  65. Ad Blocker - AdAwayTint Browser Adblock Add-on

    SECURITY -
  66. Call Recorders - Call Recorder - ACR, Call Recorder
  67. Caller Identification - Truecallerwhowho, Caller ID & Mobile Locator
  68. Anonymous Browsing - OrfoxFire.onionOrbot
  69. Anti-theft - Avast, Cerberus anti theft, Prey

    GENERAL EDUCATIONAL -
  70. Knowledge - WolframAlpha, All Wolfram Apps
  71. Maths - Math HelperFormulae Helper
  72. Chemistry - Periodic Table

    ADVANCED ENGINEERING -
  73. Scientific Calculators - MathematicsHiPER CalcGraphing Calculator PRO
  74. Electronics - ElectroDroid Pro, Electrical calculations
  75. Unit Converters - Unit Converter PlusUnit ConverterUnit Converter Pro Plus
  76. Astronomy - Mobile Observatory, Star Walk
  77. Patents - Relecura Patent Analytics

    FINANCE -
  78. Finance - XE Currency ProBarchartINVESTING.com 
  79. Personal Finance - Money Lover,  Splitwise

    BIOLOGY -
  80. Medical - Handbook of diseases
  81. Food -  E-Codes: Food Additives

    LANGUAGES -
  82. English - Vocabulary.com
  83. Learning New Languages DuolingoMemriseLuvlingua Pro

    PRODUCTIVITY/DEVELOPMENT -
  84. Make your own Apps - SketchwareApper
  85. Tools - Smart Tools, Ruler+
  86. Programming - C4droid - C/C++ compiler & IDE
  87. GestureControl - GMD GestureControl 
  88. Task Automation - Tasker

    INCREASING BATTERY LIFE -
  89. Battery Statistics - AccuBatteryBetterBatteryStats, GSam Battery Monitor
  90. AMOLED Display Mods for Battery - NOMone Resolution ChangerPixoff: Battery Saver, Always On AMOLED

    APP INSTALLATION/MODIFICATION -
  91. Bloatware Removal - System app remover
  92. App Store - F-DroidBlankStoreAptoide Lite, AppBrain App Market, Fossdroid
  93. App modifications - Lucky Patcher (Remove Google License Verification and Ads from installed Apps)
  94. Install Custom Gapps - Open GApps

    SERVICE/APPS MANAGEMENT -
  95. Background Apps Management - Hibernation Manager, Greenify (Donation Package), ForceDoze, Naptime
  96. Task/App Managers - SystemPanel
  97. Apps & Services Management/Backup - System CleanupMy Android ToolsTitanium Backup

  98. SUPERUSER ROOT/MOD MANAGEMENT -
  99. Root Permissions' Pre-requisites - SuperSUBusyBox Pro
  100. Flash/Backup/Restore Kernels & Recoveries - FlashfireFlashify
  101. All-in-One Kernel Management - Kernel Adiutor
  102. All-In-One ROM Customization/Backup - 3C ToolboxROM Toolbox Pro

Note -

Above mentioned are the Best Alternatives to Stock Apps for Android - "For High Performance and Efficient Resource Usage on Old/Legacy Phones", which have a Google Play Store rating of at least 3.5/5 (70%).

Ankit

{picture#https://image.ibb.co/dw0NN6/Linkedin.jpg} My primary objective in life is to Actualize my potential in Research, Design & Development by establishing a practical Equilibrium between Performance & Economy for products & services. I’m driven by the moral imperative to make life more livable for all beings by innovating new technologies and combining them with streamlined pre-existing technologies. You can support me on Patreon. get updates via Facebook, connect with me on Linkedin, and if interested, see my Resume. {facebook#https://www.facebook.com/AkAnkit5} {patreon#https://www.patreon.com/akankit} {twitter#https://www.twitter.com/Ak_Ankit} {youtube#https://www.youtube.com/channel/UCAcChaalQOKZ5A1kC-2B38w}
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