Here's a basic CSS file for styling your static HTML shopping list web app. This will give your application a clean and simple look:

```css
/* styles.css */

/* General styling for body */
body {
    font-family: Arial, sans-serif;
    background-color: #f8f9fa;
    margin: 0;
    padding: 0;
    display: flex;
    justify-content: center;
    align-items: center;
    height: 100vh;
}

/* Container for the shopping list */
.container {
    background-color: #ffffff;
    box-shadow: 0 4px 8px rgba(0, 0, 0, 0.1);
    border-radius: 8px;
    width: 90%;
    max-width: 400px;
    padding: 20px;
}

/* Header styling */
h1 {
    font-size: 24px;
    text-align: center;
    color: #333333;
    margin-bottom: 20px;
}

/* Input field styling */
input[type="text"] {
    width: calc(100% - 50px);
    padding: 10px;
    margin-bottom: 10px;
    border: 1px solid #dddddd;
    border-radius: 4px;
}

/* Button styling */
button {
    padding: 10px 15px;
    background-color: #28a745;
    color: #ffffff;
    border: none;
    border-radius: 4px;
    cursor: pointer;
    transition: background-color 0.3s;
}

button:hover {
    background-color: #218838;
}

/* List styling */
ul {
    list-style-type: none;
    padding: 0;
}

li {
    padding: 10px;
    border-bottom: 1px solid #dddddd;
    display: flex;
    justify-content: space-between;
    align-items: center;
}

li:last-child {
    border-bottom: none;
}

/* Remove button styling */
.remove-btn {
    background-color: #dc3545;
    color: #ffffff;
    border: none;
    border-radius: 4px;
    padding: 5px 10px;
    cursor: pointer;
    transition: background-color 0.3s;
}

.remove-btn:hover {
    background-color: #c82333;
}
```

This CSS will style your shopping list application with a simple, clean interface, making it easy for users to add and remove items from the list. You can further customize the styles to match your preferences or brand.