CPU's have gone a very long way since Pentium4's
Any of today's lowest end cpu is miles ahead of a Pentium 4
It is hard to make a recommendation because I am not sure what your budget is like and I am not sure if you rather buy a name brand, get someone to build it or to build it yourself.
I recommend that you build it yourself or you go to a "microbytes, or any computer only store that builds pc's"
You will want the following
A pentium G630 or G850 (about 70 to 80$ cpu)
Those are the Pentium 4's of today (if not the celerons of today but perform astonishingly well)
You can also get a Core I3.
If you go AMD, you can go for a phenom X4 if still in stock or an FX43XX
I would recommend an AMD A8 or A10 as they bring better balance for processing and video.
No matter what CPU you use, let it be a higher end Intel Core I5 to a lower end AMD FX4350
You will not see a massive difference in computer operation.
A computer can only go as fast as it can read the information given to it.
For the best computing experience, I STRONGLY suggest, you get a computer with an SSD Harddrive.
something like 180Gig or 256Gig ssd hard drive. (if you need more space, get a regular drive on the side for storage)
If you plan on building it yourself let us know and I am sure someone can make a full list of parts for you.