New Computer?

Things to consider: 

• Generally you get what you pay for, i.e., low priced computers will be slow.
• When you purchase a new machine, it will now be Windows 10.  If you have older applications, check the manufacturer's requirements!  You may end up upgrading those as well..
• Look out for setup charges.  Find out what they include.  Starting a new computer and getting Windows set up is almost automatic, there is no need to pay for that service.  If on the other hand they activate Microsoft Office, the Antivirus application, etc. and get all available updates, then a small charge may be worthwhile.  Contrary to appearance during setup, you do not have to set up or supply an email address!  See this.
• Most computers come with the Microsoft Office but you will have to pay for it!  Note: If you are looking for Outlook for email, you need the Business edition...
• Extended warranties.  Look at the cost of the extended warranty, then decide.  But if you have kids, you may want to consider an accident damage warranty for Laptops.

Restore media:  Manufacturers do not include this anymore, but do have a utility to create it. 
Do so immediately!  Put that media as well as any "product key" cards in a safe place!

With that out of the way, here are our thoughts on minimum specifications:

Processor

This is the price swing.  We recommend Intel's i5, i7 or better.  You may consider AMD's new Ryzen processor (article).  But certainly avoid low end processors like the Celeron and i3 processor.  They are slow!

If you will be working with images, movies or are a gamer, consider the fastest available Intel processor, otherwise look at 2 or 3 generation older processors.   Almost a bit overwhelming, but here is a chart comparing processors.

Memory

4 Gb minimum for typical home and Internet use, but more is always better!

Hard drive

They are so large these days, this isn't even an issue, but consider getting an external drive for backups.  If a laptop, especially one that's moved around a lot, you should consider a solid state hard drive.  But SSDs are still somewhat small.  If you have a lot of pictures and/or music, the drive may quickly become full.

Monitor

Desktop: Today's standard is the 19+ inch wide panel.  Before you buy a "touch screen", think about your desk.  Touch screens are nice however, they would have to be placed close enough to the front of the desk to use at which point they may be too close to view.

Laptop: Display/Monitor There may be a few choices here other than just the size.  Be aware that while the glossy finish screens look nice, they are very hard to view in brightly lighted/outdoor environments.  Also: A lot of laptops are now coming with ultrathin monitors - that can easily cracked if not handled with care.  When opening and closing these, use both top corners or the center.  Opening from one corner allows these to flex and can lead to a cracked LCD.

Graphics Card

Generally the OEM built-in is fine for typical business, home and Internet use.  However, if you want to play games you should seriously consider the fastest available video card. 

Other items

CD/DVD burner.   Data/Fax modem - If you have or are getting DSL, a dialup modem will not be needed unless you need fax capabilities directly from the computer and even then, most multi-function printers can do the faxing.

Case Design

While not as important, it is something to think about. The traditional "tower" generally means replacement parts are generic and readily available whereas the "small or mini" towers and especially the "all-in-one" units may require OEM parts.

Finally:  Get a battery backup device (UPS) preferably with phone line protection for your DSL or modem...  The computer's power supply and hard drive are especially prone to failure in the event of a power outage.  It does not take a power surge such as during a thunder storm.  A simple drop in power can cause damage!