Here is a good comparison on the differences to compare whether AMD, Intel, Celeron, etc.
1) RAM - Cheapest way to increase performance. Yes I would pay up for this, well worth it imo.
2) Processor Speed - It matters if one is twice as much as the other, it will list the speed so I would always check this. If they are close it may not matter much, #1 and #4 matter much more to me.
3) Hard drive size - Probably doesnt matter today, hard drives are HUGE and I typically dont even use 25% of my hard drive space. Not worth paying up for larger unless you are doing something unusual to consume tons of hard drive space.
Although keep in mind solid state drives are advanced drives, faster and more stable, so you will see higher cost on those, and those are worth the upgrade imo but also are smaller in size so you need to weigh the costs vs your use etc.
3) Cache memory / bus speed - Yes this matters. If one is twice the size of the other, you probably are paying more for it but this improves speed. I usually would pay up for this.
4) Video memory - This matters alot if PC is used for gaming. Integrated graphics is worse, you will pay up for better graphics cards but well worth it if gaming. If not gaming then it wont matter much for viewing videos, youtube, that type of stuff .... but I would compare these vs price.
5) Miscellaneous stuff like software, usb ports, hdmi output, card readers, etc is really up to you. These just depend what you have or plan on using it for etc.
If laptop instead of desktop computer:
Screen size - This matters alot, for example 17 inch vs 15 inch, so you may want to pay more for 1 vs the other, thats up to you.
Battery Power - This may matter if you travel alot so its worth comparing, otherwise if you just leave it plugged in all the time then battery wont matter.