A simple procedure would be to press `[ to jump to the start of the text you last changed. For example, you may use ciw to change inner word, or p to paste, then scroll elsewhere. Typing `[ would jump to the start of the word you just changed, or to the start of the text you just pasted (see marks).
To select the last changed text (or the text that was just pasted), use a mapping like this in your vimrc:
nnoremap gp `[v`]
After pasting, type gp to select the pasted text in visual mode. This is similar to the standard gv which you can type to select the last visually-selected text.
Following is a more elaborate alternative:
nnoremap <expr> gp '`[' . strpart(getregtype(), 0, 1) . '`]'
With this alternative, typing gp will select the last changed (or pasted) text, and the visual mode will be the same as was last used. For example, you may press v to start character-wise visual selection, then move the cursor and press y to yank (copy) the selected text. Elsewhere, you may press p to paste the text. In that case typing gp would select the pasted text character-wise.
Repeating this example, but using V would use line-wise visual selection (whole lines would be selected). Similarly, using Ctrl-V (or Ctrl-Q if you use Ctrl-V for pasting) would use block-wise visual selection.
The mapping uses "<expr>" which means that when you type gp, the mapping is evaluated as an expression, then the result is used. The dot operator (.) is used to concatenate three strings. The first string (without quotes) is `[ and the third string is `]. The second string is the first character (:help strpart()) of the result from calling getregtype() which is the "type" of the last register used in a normal mode command. The type is 'v', 'V', or Ctrl-V depending on whether the text in the register resulted, respectively, from a character, a line, or a block operation. (:help getregtype())
For example, if you type yiw to copy a word, the function getregtype() will return v, and the result of the mapping expression will be `[v`] (the same as the first mapping given above). However, if you type 3Y to copy three lines, the result will be `[V`] (linewise).