bpo-39041: Add GitHub Actions badge to README.rst (GH-17628)

Also skip build for doc-only changes and enable on push
diff --git a/.github/workflows/build.yml b/.github/workflows/build.yml
index 16d6f0d..7f13cfb 100644
--- a/.github/workflows/build.yml
+++ b/.github/workflows/build.yml
@@ -1,14 +1,16 @@
 name: Tests
 
 on:
-  #push:
-  #  branches:
-  #  - master
-  #  - 3.8
-  #  - 3.7
-  #  paths-ignore:
-  #  - 'Doc/**'
-  #  - 'Misc/**'
+  push:
+    branches:
+    - master
+    - 3.8
+    - 3.7
+    paths-ignore:
+    - 'Doc/**'
+    - 'Misc/**'
+    - '**/*.md'
+    - '**/*.rst'
   pull_request:
     branches:
     - master
@@ -17,6 +19,8 @@
     paths-ignore:
     - 'Doc/**'
     - 'Misc/**'
+    - '**/*.md'
+    - '**/*.rst'
 
 jobs:
   build_win32:
diff --git a/README.rst b/README.rst
index 62dd0fd..43f6197 100644
--- a/README.rst
+++ b/README.rst
@@ -5,6 +5,10 @@
    :alt: CPython build status on Travis CI
    :target: https://travis-ci.org/python/cpython
 
+.. image:: https://github.com/python/cpython/workflows/Tests/badge.svg
+   :alt: CPython build status on GitHub Actions
+   :target: https://github.com/python/cpython/actions
+
 .. image:: https://dev.azure.com/python/cpython/_apis/build/status/Azure%20Pipelines%20CI?branchName=master
    :alt: CPython build status on Azure DevOps
    :target: https://dev.azure.com/python/cpython/_build/latest?definitionId=4&branchName=master