Hi, Jamie.
The HP Envy Phoenix desktop on that page should do okay with The Sims 3 at high settings - with the caveat that the system may strain on the graphics. The nVidia GeForce GT 640 card is a budget gaming card and doesn't really have the oomph needed to play the game at full HD with all the eye candy enabled.
The problem? The graphics card is an entry level card with a decent Graphics Processing Unit (GPU). Normally the GPU in the 600 and 700 series cards is pretty decent. Where this card is hamstrung is the type of memory they decided to use with the card - DDR3 is the slowest graphics memory available. This is the same memory as your computer uses and while fast for general purpose, the more dedicated GDDR3 and GDDR 5 memory outperforms it. While it includes 4 GB of memory, it may still under perform due to the lower speed.
The computer's Central Processing Unit (CPU) is a very good processor - MrsFlynn and I have the same processor in our desktops. Here would be my suggestion - if you have the budget, get the ENVY Phoenix and save up for a better graphics card. The
nVidia GeForce GTX 750 Ti with 2 GB of GDDR5 memory (the fastest dedicated graphics memory) is about $150 from Amazon. Be aware that cards like the GTX 750 will require a power connection. If your computer's power supply doesn't have such a connection, you will need to replace the power supply in order to use the newer graphics card. A 600 watt power supply is about $50, so it's not too expensive. Have a local computer friend help you install it.
By the way, I discovered the
ENVY Phoenix is about $200 cheaper at Amazon. If you plan to buy in-store, Best Buy will price match if you ask.
For the monitor, I would check them out in store and see what looks good to you. Make sure you look at it from different angles and see about how far to the sides, top and bottom you can be before the colors start to look funky. LCD monitors have come way down in price and way up in quality over the last several years, but there are still some duds out there. Another option is a small HDTV - MrsFlynn uses a 22" Vizio TV as a monitor, for example.
Hope this helps and happy Simming!
Flynn