Information
So on booting DMC3 I noticed the game has a terrible outdated use of controller support, after messing around trying various methods I created a set-up that's in my opinion a great alternative to the boring Keyboard & Mouse.

note - If manual doesn't work out for you please use xpadder.

Manual Config
First navigate to the following within your steam folder game root.
C:\Program Files\Steam\steamapps\common\Devil May Cry 3\DMC3SE.ini
This notepad contains all the vanilla accepted controllers that originally with the game, you'll need to find the computer recognised controller name which can be found in your computers device manager for example = XBOX 360 Wireless Receiver for Windows
You'll need to then write in your controllers name and your custom gamepad key/s you wish to use like so.

[Controller (XBOX 360 Wireless Receiver for Windows)]
START = 7
SELECT = 6
CIRCLE = 1
TRIANGLE = 3
SQUARE = 2
CROSS = 0
L1 = 4
R1 = 5
L2 = 11
R2 = 12
L3 = 8
R3 = 9
L<->R = 2

Fullscreen
ALT + Enter
or if you wish for fullscreen on start up,
Navigate to - C:\Program Files\Steam\steamapps\common\Devil May Cry 3\DMC3SE.ini
and adjust the WINDOW_STATE to your monitors resolution

Xpadder ALTERNATIVE
First of all I highly recommend for any modern gamer to grab a copy of Xpadder when it comes to playing video games that may not have controller support, the program in my experiance has been the most user friendly/safe, keyboard to controller application around. Xpadder accepts most if not all "non-dodgey" controllers such as the PS3 or an Xbox360 joysticks.
An alternative is Motion-Joy mentioned in another DM3 guide but is a lot less polished compared to this program.
Xpadder Site Link [www.xpadder.com]
If you don't know how to use Xpadder there's various support and help wiki/guides around the net and on their site.

* It's important to revert all settings you've currently changed back to the default as this setup uses them.

Controller Map - PS3/XBOX - Example
Cross/A - K
Square/X - I
Circle/B - L
Triangle/Y - 0

DPad Up - 1
DPad Left - 2
DPad Right - 4
Dpad Down - 3

L1/LB - Q
L2/LT - Space
R1/RB - E
R2/RT - J

Start - N
Select - M

Any questions you have reguarding the guide or extra help your need please write it in the comments or send me a message.
I often use Steam so I'll be sure to help.