I run a spec racing series on Tuesday night at 7:00pm central. We are halfway thru our thirteenth season right now. This seasons car is the 2014 Alfa Romeo 4C. Everyone runs the same car with the same upgrades, but tuning is allowed. We also run simulation damage. If this sounds like something you are interested in here is a link to our reddit page with all the information for the current season.
There’s quite a few Top 10 / Top 20 teams on Forza that come to mind right now, but something to consider is your skill level. Beating Unbeatable CPU is a good metric to show that you’re actually a competent driver (if this however requires using the rewind feature in races then its nothing impressive).
This is the important part
Teams are not too big on taking on anyone new right now. This is because of the upcoming Forza Racing Championship by Forza Motorsport themselves, starting next Monday. For anyone short of knowledge on the championship and who are yet to register, visit here ASAP: https://forzarc.gfinity.net/ In short, the ForzaRC is the largest tournament/championship series that exists in the franchise and its the #1 place to try showing yourself to other drivers and teams around the world. I got noticed by quite a few teams after appearing in the ForzaRC Season 2 last year as its highly competitive and getting yourself even just in the Top 200 of each event is somewhat remarkable.
Now, teams won’t want to bother taking on new people if they (1) have no idea who the person is and (2) have no idea how good they are. With this said, the best advice anyone can give is that you sign up, give this ForzaRC a good go and then you’ll get a much clearer perspective on not only how good you currently are on the game, but also how that skill level can blend with some of the many teams in the Forza community.
Considering you like P Class and the Modern GT cars in R Class and (assuming) you want to get better at the game whilst on limited play time on Fridays and Saturdays as you said, the one team I can really recommend you give a look is THR | Team Highlands Racing. They compete very regularly in league events (Online Racing League is a very popular one: http://onlineracingleague.proboards.com/forum), have a great bunch of drivers who are sociable, friendly and never short of providing help for others throughout the community.
Keep us updated here on what you do and if you take on the ForzaRC. The one particular aspect of the event you should concentrate on given your limited availability is the 1v1 racing series each Saturday. See here for the car and track combos starting next week 7th May, halfway down the page: https://forzarc.gfinity.net/elite/rules
Good luck and let us know if there’s anything else you need!
