Almost any TV or monitor with an HDMI or DVI input will work fine. I have used my Pi computers on televisions and monitors with resolutions of full HD (1920x1080p), 1680x1050, 1440x900, 1366x768, 1280x1024 and 1024x768 without a hitch.
If you have a black border around the screen, turn off overscan compensation (which is normally needed with TV, but not monitors). Some screens may require a bit of tweaking if the EDID data is not read correctly. In most cases the Pi will configure the resolution automatically.
For a DVI monitor a direct HDMI-DVI cable is the best option. While I have successfully used HDMI-DVI adapters, others have had problems with them, so avoiding adapters may save you some trouble.
Depending on what you normally do on a "simple computer" you may find even the Pi 3B+ on the slow side. Using one of the new "A1" class micro SD cards can help. I like the new SanDisk Ultra A1 cards because they are affordable and perform well. I mostly use 32GB cards, as they have a good price, performance ratio, and should have enough capacity for most projects (you can add a USB drive later if you need more).
A good power supply is a must. Phone chargers are not recommended, and unfortunately many power supplies advertised for the Pi are just re-purposed pone chargers. The official Raspberry Pi Universal Power Supply is reasonably priced and a proven performer. Click on the green BUY tag above and scroll down a bit.
I own several Pi computers from the old model B up to the latest 3B+ and all 3 models of the Pi Zero. The current version of Raspbian Stretch is compatible with all models available to date. Ubuntu Mate 16.04 is not compatible with the newer 3B+ and 3A+ models which require a new kernel and firmware, but both Ubuntu and Raspbian are based on Debian/GNU Linux, so you shouldn't find the learning curve too steep.
Welcome to the Raspberry Pi community! The people who volunteer their time here to support this amazing little computer are one of the reasons it has become so popular.
My mind is like a browser. 27 tabs are open, 9 aren't responding,
lots of pop-ups...and where is that annoying music coming from?