As others said above, you have to see what works for you. I'm a hill climber, Love out of the saddle climbing. I have also been riding fix gear a long time. Long enough tha the reality that I am no longer a 20 something has sunk in.

I started riding in an 81" gear. (For gear inches, divide chainring teeth by cog teeth and multiple by wheel diameter. For road 700c, use 27". So 42 /14 X 27 = 81" for example.) The vets in my racing club quickly told me to reduce my gear to 42-17, 16 as I got strong through the season, (By the season end, as a strong racer, I was riding a 15.) I was strong enough to climb just about anything (at real cost!) with those gears. Now, coming down I always had brakes. In those days, it never seriously occurred to most of us to ride without. We were riding for training and brakes allowed us to ride faster (better training) and avoid crashes (potentially real setbacks in that same training).

So my advice? Have a lockring spanner and chain whip, put on a smallish chainring (42,43 or 44) and buy several cogs. 15 through 18 would be a good start. Experiment. When you look at your next rear wheel, seriously consider a flip-flop hub, fix-fix. Then you can leave for your ride with say a 16 and a 17, You can even go totally crazy like I did 7 years ago and have a custom fix gear made that you can run from 12 to 24 teeth on and buy all the cogs. Carrying a chainwhip, I can ride up true mountains then come down in a gear that is really fun. (That bike has ridden to, up and around Crater Lake.) But like fix gears 100 years ago, I have to plan ahead. It takes me 2 minutes to flip my wheel and 5 to change out a cog. I still do a lot of hills the old way, grunt up and spin down just like when I started 42 years ago (almost exactly today!)

If you haven't gotten very far into buying cogs and chainrings, seriously consider going to an all 1/'/8" setup. (There are two single spee/fix gear standards: 3/32" which is the 1960s and '70s 10-speed standard chain and gear teeth width and 1/8" which is the oldest standard and still used on kids single speeds, IGH setups and on the track. (Both are used on the track, but the 1/8" is more common and the preferred for the stronger riders. 1/8"{ has two advantages for you: longer wearing - both chain and gear teeth - and more resistance to being thrown off when spinning fast - a bigger issue for riding road hills than on the velodrome.

I'm guessing you are relatively new to fix gear riding. Welcome! It's a great journey!

Ben