I am more of an observer of wildlife in general and not specifically birds, so record any living wild animal I see. Having said that birds are a favorite and of the 974 animals that I have seen in the wild on my list as of today, 730 are birds. It is easier to see birds than most other animals and there is a lot of help available in the form of guide books, guides, web sites etc that also make it easier. I have also noted that there is an issue accommodating both birdwatching, which can require early mornings, with mammal watching, which can require late nights, on the same trip.
I have only taken it seriously in the last two years. For many years I did not even have a decent pair of binoculars, and only bought a pair for a trip I did to Komodo National Park, and a subsequent stay in Bali in November 2017. A trip to South Africa in 2018 allowed a few days in Chobe National Park, Botswana, and I was hooked. In total I saw 17 species of mammal and 70 species of bird in Chobe. I do travel a lot for business so always try to find a little time, usually for birdwatching, wherever I am. The only trips, other than day trips around home, that I can recall were specifically for wildlife were that to Komodo and one to Sri Lanka this February. I hope to do a lot more when we all get over Covid-19. I don't take trips to chase specific rarities (except maybe the Komodo dragon) but have visited a couple of sites especially when they have conservation related species.
Regarding equipment I do think a pair of decent binoculars are important, otherwise it can all be very frustrating. I also recently acquired a fairly decent camera with a long lens, and that does add to the enjoyment. As for a scope, I had never used one till I had the opportunity to do so on a couple of occasions earlier this year. I can certainly see their usefulness however the extra weight is an issue given how vicious airlines are now over baggage. I have also turned into a great purchaser of guide books, and use them for planning and dreaming as well as in the field. More and more I have become in favour of using local guides when available. I am only in overseas destinations for a short period of time and it has cost me a lot of money to get there, so if a guide can help me get the most out of my visit I am all for it. Lastly web sites like ebird and mammal.com and trip reports on sites like this are extremely useful to help plan trips.
I started my list on my return from Africa and decided I did not want to lose the list I had from that trip so entered the list on an Excel spreadsheet. I added in my Komodo trip, a couple of older lists I found, went through my photos and then added any animal I had a specific memory of seeing in the wild. It is not a life list, because I started it too late in my life. Animal species are listed by Phylum, Class, Order, Family then alphabetically by scientific name. Next column is the common name and then the conservation status. Using the freeze pane function the species list is always in view. Each location is given a column and again a freeze pane at the top of the column gives the location and date. I put an "X" in each cell at the intersection of the species and the location I saw it. If it is introduced I put an "I" and feral a "F". I do record some significant species that I don't see alive but do see a carcass, a track or hear a call, for instance with "D" for dead and so on. However I don't count these. Thus it is very easy to find where I saw a certain species, or what I saw at a certain location. I don't record subspecies but because I have locations it is easy enough to work out which subspecies I have seen. Being a spreadsheet it is also very easy to work with. For instance I have just rearranged the bird taxonomy in line with "Bird Families of the World".
I should also say that I do a lot of local wildlife watching, and am currently looking out the window over our wetland. Much of my overseas wildlife watching is also in cities, it is amazing what you can find in cities such as Los Angeles and Toronto.