I live in Washington DC, so I've never made a connection of any type here. I haven't had any awful experiences getting through Immigration or retrieving luggage at IAD, but we all know that timing can vary.
The good news is that there's Metro (subway) service between the airports with just one change required. Although there's occasionally an escalator or elevator out of service, it would be extremely unusual for both forms of intra-station transportation to be unavailable, so I wouldn't worry about that aspect of the transfer as long as you can manage your luggage on an escalator, if necessary.
Significant system issues causing noticeable delays are sort of unusual, but I can't say they're unheard-of.
There's a lot of Metro info available here:
https://www.wmata.com/service/rail/
On my PC there's a small, clickable "Trip Planner" block near the left margin of that webpage. Use "Ronald Reagan Washington National Airport" as your destination.
WMATA suggests taking the Silver Line in the direction of Largo or New Carrollton, getting off at Rosslyn and taking a Blue Line train in the direction of Franconia-Springfield. That is the shortest route and will take roughly 82 minutes (depending on the transfer time required at Rosslyn).
You should be able to use a credit card to tap as you enter the fare gate at the beginning of the trip and exit at the end of the trip. The current fare is $6.75.
Google Maps gives a driving time between the two airports of between 35 and 85 minutes for mid-afternoon departure on a workday. You could check the WMATA website for service delays while in line at Immigration or waiting for your luggage and make a call about taking a taxi at that point if it seems better (assuming no weather issues that could affect traffic).